# Chapter 06 What is the probability that the stock price will be more than

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Test Prep

Book Title

Essentials of Modern Business Statistics 4th (Fourth) Edition By Williams 4th Edition

Authors

J.K

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Exhibit 6-7

f(x) =(1/10) e-x/10 x 0

92. Refer to Exhibit 6-7. The mean of x is

a. 0.10

b. 10

c. 100

d. 1,000

93. Refer to Exhibit 6-7. The probability that x is less than 5 is

a. 0.6065

b. 0.0606

c. 0.3935

d. 0.9393

94. Refer to Exhibit 6-7. The probability that x is between 3 and 6 is

a. 0.4512

b. 0.1920

c. 0.2592

d. 0.6065

95. Excel’s EXPONDIST function can be used to compute

a. exponents

b. exponential probabilities

c. cumulative exponential probabilities

d. Both exponential probabilities and cumulative exponential probabilities are

correct.

96. Excel’s EXPONDIST function has how many inputs?

a. 2

b. 3

c. 4

d. 5

97. When using Excel’s EXPONDIST function, one should choose TRUE for the third input

if

a. a probability is desired

b. a cumulative probability is desired

c. the expected value is desired

d. the correct answer is desired

PROBLEMS

1. A random variable x is uniformly distributed between 45 and 150.

a. Determine the probability of x = 48.

b. What is the probability of x 60?

c. What is the probability of x 50?

d. Determine the expected vale of x and its standard deviation.

2. The price of a bond is uniformly distributed between $80 and $85.

a. What is the probability that the bond price will be at least $83?

b. What is the probability that the bond price will be between $81 and $90?

c. Determine the expected price of the bond.

d. Compute the standard deviation for the bond price.

3. The price of a stock is uniformly distributed between $30 and $40.

a. What is the probability that the stock price will be more than $37?

b. What is the probability that the stock price will be less than or equal to $32?

c. What is the probability that the stock price will be between $34 and $38?

d. Determine the expected price of the stock.

e. Determine the standard deviation for the stock price.

4. The time it takes to hand carve a guitar neck is uniformly distributed between 110 and

190 minutes.

a. What is the probability that a guitar neck can be carved between 95 and 165

minutes?

b. What is the probability that the guitar neck can be carved between 120 and 200

minutes?

c. Determine the expected completion time for carving the guitar neck.

d. Compute the standard deviation.

5. The length of time it takes students to complete a statistics examination is uniformly

distributed and varies between 40 and 60 minutes.

a. Find the mathematical expression for the probability density function.

b. Compute the probability that a student will take between 45 and 50 minutes to

complete the examination.

c. Compute the probability that a student will take no more than 40 minutes to

complete the examination.

d. What is the expected amount of time it takes a student to complete the

examination?

e. What is the variance for the amount of time it takes a student to complete the

examination?

6. The advertised weight on a can of soup is 10 ounces. The actual weight in the cans

follows a uniform distribution and varies between 9.3 and 10.3 ounces.

a. Give the mathematical expression for the probability density function.

b. What is the probability that a can of soup will have between 9.4 and 10.3 ounces?

c. What is the mean weight of a can of soup?

d. What is the standard deviation of the weight?

7. The length of time patients must wait to see a doctor in a local clinic is uniformly

distributed between 15 minutes and 2 1/2 hours.

a. Define the random variable in words.

b. What is the probability of a patient waiting exactly 50 minutes?

c. What is the probability that a patient would have to wait between 45 minutes and

2 hours?

d. Compute the probability that a patient would have to wait over 2 hours.

e. Determine the expected waiting time and its standard deviation.

8. For the standard normal distribution, determine the probability of obtaining a z value

a. greater than zero.

b. between -2.34 to -2.55

c. less than 1.86.

d. between -1.95 to 2.7.

e. between 1.5 to 2.75.

9. Z is a standard normal random variable. Compute the following probabilities.

a. P(-1.33 z 1.67)

b. P(1.23 z 1.55)

c. P(z 2.32)

d. P(z -2.08)

e. P(z -1.08)

10. Z is a standard normal random variable. Compute the following probabilities.

a. P(-1.23 z 2.58)

b. P(1.83 z 1.96)

c. P(z 1.32)

d. P(z 2.52)

e. P(z -1.63)

f. P(z -1.38)

g. P(-2.37 z -1.54)

h. P(z = 2.56)

11. Z is a standard normal variable. Find the value of z in the following.

a. The area between 0 and z is 0.4678.

b. The area to the right of z is 0.1112.

c. The area to the left of z is 0.8554

d. The area between -z and z is 0.754.

e. The area to the left of -z is 0.0681.

f. The area to the right of -z is 0.9803.

12. The miles-per-gallon obtained by the 1995 model Q cars is normally distributed with a

mean of 22 miles-per-gallon and a standard deviation of 5 miles-per-gallon.

a. What is the probability that a car will get between 13.35 and 35.1 miles-per-

gallon?

b. What is the probability that a car will get more than 29.6 miles-per-gallon?

c. What is the probability that a car will get less than 21 miles-per-gallon?

d. What is the probability that a car will get exactly 22 miles-per-gallon?

13. The salaries at a corporation are normally distributed with an average salary of $19,000

and a standard deviation of $4,000.

a. What is the probability that an employee will have a salary between $12,520 and

$13,480?

b. What is the probability that an employee will have a salary more than $11,880?

c. What is the probability that an employee will have a salary less than $28,440?

14. A major department store has determined that its customers charge an average of $500

per month, with a standard deviation of $80. Assume the amounts of charges are

normally distributed.

a. What percentage of customers charges more than $380 per month?

b. What percentage of customers charges less than $340 per month?

c. What percentage of customers charges between $644 and $700 per month?

EMBS4 TB06 - 20

15. The contents of soft drink bottles are normally distributed with a mean of twelve ounces

and a standard deviation of one ounce.

a. What is the probability that a randomly selected bottle will contain more than ten

ounces of soft drink?

b. What is the probability that a randomly selected bottle will contain between 9.5

and 11 ounces?

c. What percentage of the bottles will contain less than 10.5 ounces of soft drink?

16. The life expectancy of computer terminals is normally distributed with a mean of 4 years

and a standard deviation of 10 months.

a. What is the probability that a randomly selected terminal will last more than 5

years?

b. What percentage of terminals will last between 5 and 6 years?

c. What percentage of terminals will last less than 4 years?

d. What percentage of terminals will last between 2.5 and 4.5 years?

e. If the manufacturer guarantees the terminals for 3 years (and will replace them if

they malfunction), what percentage of terminals will be replaced?

17. Scores on a recent national statistics exam were normally distributed with a mean of 80

and a standard deviation of 6.

a. What is the probability that a randomly selected exam will have a score of at

least 71?

b. What percentage of exams will have scores between 89 and 92?

c. If the top 2.5% of test scores receive merit awards, what is the lowest score

eligible for an award?

d. If there were 334 exams with scores of at least 89, how many students took the

exam?

18. The average starting salary for this year's graduates at a large university (LU) is $30,000

with a standard deviation of $8,000. Furthermore, it is known that the starting salaries

are normally distributed.

a. What is the probability that a randomly selected LU graduate will have a starting

salary of at least $30,400?

b. Individuals with starting salaries of less than $15,600 receive a low income tax

break. What percentage of the graduates will receive the tax break?

c. What are the minimum and the maximum starting salaries of the middle 95% of

the LU graduates?

d. If 303 of the recent graduates have salaries of at least $43,120, how many

students graduated this year from this university?

19. The weights of items produced by a company are normally distributed with a mean of 4.5

ounces and a standard deviation of 0.3 ounces.

a. What is the probability that a randomly selected item from the production will

weigh at least 4.14 ounces?

b. What percentage of the items weighs between 4.8 and 5.04 ounces?

c. Determine the minimum weight of the heaviest 5% of all items produced.

d. If 27,875 of the items of the entire production weigh at least 5.01 ounces, how

many items have been produced?

20. The life expectancy of Timely brand watches is normally distributed with a mean of four

years and a standard deviation of eight months.

a. What is the probability that a randomly selected watch will be in working

condition for more than five years?

b. The company has a three-year warranty period on their watches. What

percentage of their watches will be in operating condition after the warranty

period?

c. What is the minimum and the maximum life expectancy of the middle 95% of the

watches?

d. Ninety-five percent of the watches will have a life expectancy of at least how

many months?

21. The weights of the contents of cans of tomato paste produced by a company are normally

distributed with a mean of 6 ounces and a standard deviation of 0.3 ounces.

a. What percentage of all cans produced contains more than 6.51 ounces of tomato

paste?

b. What percentage of all cans produced contains less than 5.415 ounces?

c. What percentage of cans contains between 5.46 and 6.495 ounces?

d. Ninety-five percent of cans will contain at least how many ounces?

e. What percentage of cans contains between 6.3 and 6.6 ounces?

22. A professor at a local university noted that the grades of her students were normally

distributed with a mean of 78 and a standard deviation of 10.

a. The professor has informed us that 16.6% of her students received grades of A.

What is the minimum score needed to receive a grade of A?

b. If 12.1% of her students failed the course and received Fs, what was the

maximum score among those who received an F?

c. If 33% of the students received grades of B or better (i.e., As and Bs), what is the

minimum score of those who received a B?

23. "DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality

control department has noted that the bottles of vitamins marked 6 ounces vary in content

with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally

distributed.

a. What percentage of all bottles produced contains more than 6.51 ounces of

vitamins?

b. What percentage of all bottles produced contains less than 5.415 ounces?

c. What percentage of bottles produced contains between 5.46 and 6.495 ounces?

d. Ninety-five percent of the bottles will contain at least how many ounces?

e. What percentage of the bottles contains between 6.3 and 6.6 ounces?

24. The daily dinner bills in a local restaurant are normally distributed with a mean of $28

and a standard deviation of $6.

a. Define the random variable in words.

b. What is the probability that a randomly selected bill will be at least $39.10?

c. What percentage of the bills will be less than $16.90?

d. What are the minimum and maximum of the middle 95% of the bills?

e. If twelve of one day's bills had a value of at least $43.06, how many bills did the

restaurant collect on that day?

25. The monthly income of residents of Daisy City is normally distributed with a mean of

$3000 and a standard deviation of $500.

a. Define the random variable in words.

b. The mayor of Daisy City makes $2,250 a month. What percentage of Daisy

City's residents has incomes that are more than the mayor’s?

c. Individuals with incomes of less than $1,985 per month are exempt from city

taxes. What percentage of residents is exempt from city taxes?

d. What are the minimum and the maximum incomes of the middle 95% of the

residents?

e. Two hundred residents have incomes of at least $4,440 per month. What is the

population of Daisy City?

26. The average starting salary of this year’s MBA students is $35,000 with a standard

deviation of $5,000. Furthermore, it is known that the starting salaries are normally

distributed. What are the minimum and the maximum starting salaries of the middle 95%

of MBA graduates?

27. A local bank has determined that the daily balances of the checking accounts of its

customers are normally distributed with an average of $280 and a standard deviation of

$20.

a. What percentage of its customers has daily balances of more than $275?

b. What percentage of its customers has daily balances less than $243?

c. What percentage of its customers' balances is between $241 and $301.60?

28. The weekly earnings of bus drivers are normally distributed with a mean of $395. If only

1.1% of the bus drivers have a weekly income of more than $429.35, what is the value of

the standard deviation of the weekly earnings of the bus drivers?

29. The monthly earnings of computer programmers are normally distributed with a mean of

$4,000. If only 1.7 percent of programmers have monthly incomes of less than $2,834,

what is the value of the standard deviation of the monthly earnings of the computer

programmers?

30. The Globe Fishery packs shrimp that weigh more than 1.91 ounces each in packages

marked" large" and shrimp that weigh less than 0.47 ounces each into packages marked

"small"; the remainder are packed in "medium" size packages. If a day's catch showed

that 19.77% of the shrimp were large and 6.06% were small, determine the mean and the

standard deviation for the shrimp weights. Assume that the shrimps' weights are

normally distributed.

31. In grading eggs into small, medium, and large, the Linda Farms packs the eggs that weigh

more than 3.6 ounces in packages marked "large" and the eggs that weigh less than 2.4

ounces into packages marked "small"; the remainder are packed in packages marked

"medium." If a day's packaging contained 10.2% large and 4.18% small eggs, determine

the mean and the standard deviation for the eggs' weights. Assume that the distribution of

the weights is normal.

32. A manufacturing process produces items whose weights are normally distributed. It is

known that 22.57% of all the items produced weigh between 100 grams up to the mean

and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard

deviation.

33. Z is the standard normal random variable. Use Excel to calculate the following:

a. P(z 2.5)

b. P(0 z 2.5)

c. P(-2 z 2)

d. P(z -0.38)

e. P(z 1.62)

f. z value with .05 in the lower tail

g. z value with .05 in the upper tail

34. X is a normally distributed random variable with a mean of 50 and a standard deviation of

5. Use Excel to calculate the following:

a. P(x 45)

b. P(45 x 55)

c. P(x 55)

d. x value with .20 in the lower tail

e. x value with .01 in the upper tail

35. The time it takes a mechanic to change the oil in a car is exponentially distributed with a

mean of 5 minutes.

a. What is the probability density function for the time it takes to change the oil?

b. What is the probability that it will take a mechanic less than 6 minutes to change

the oil?

c. What is the probability that it will take a mechanic between 3 and 5 minutes to

change the oil?

36. The time it takes a worker on an assembly line to complete a task is exponentially

distributed with a mean of 8 minutes.

a. What is the probability density function for the time it takes to complete the task?

b. What is the probability that it will take a worker less than 4 minutes to complete

the task?

c. What is the probability that it will take a worker between 6 and 10 minutes to

complete the task?

37. The time between arrivals of customers at the drive-up window of a bank follows an

exponential probability distribution with a mean of 10 minutes.

a. What is the probability that the arrival time between customers will be 7 minutes

or less?

b. What is the probability that the arrival time between customers will be between 3

and 7 minutes?

38. The time required to assemble a part of a machine follows an exponential probability

distribution with a mean of 14 minutes.

a. What is the probability that the part can be assembled in 7 minutes or less?

b. What is the probability that the part can be assembled between 3.5 and 7

minutes?

39. The time it takes to completely tune an engine of an automobile follows an exponential

distribution with a mean of 40 minutes.

a. Define the random variable in words.

b. What is the probability of tuning an engine in 30 minutes or less?

c. What is the probability of tuning an engine between 30 and 35 minutes?

40. X is a exponentially distributed random variable with a mean of 10. Use Excel to

calculate the following:

a. P(x 15)

b. P(8 x 12)

c. P(x 8)

41. The Harbour Island Ferry leaves on the hour and at 15-minute intervals. The time, x, it

takes John to drive from his house to the ferry has a uniform distribution with x between

10 and 20 minutes. One morning John leaves his house at precisely 8:00a.m.

a. What is the probability John will wait less than 5 minutes for the ferry?

b. What is the probability John will wait less than 10 minutes for the ferry?

c. What is the probability John will wait less than 15 minutes for the ferry?

d. What is the probability John will not have to wait for the ferry?

e. Suppose John leaves at 8:05a.m. What is the probability John will wait (1) less

than 5 minutes for the ferry; (2) less than 10 minutes for the ferry?

f. Suppose John leaves at 8:10a.m. What is the probability John will wait (1) less

than 5 minutes for the ferry; (2) less than 10 minutes for the ferry?

g. What appears to be the best time for John to leave home if he wishes to maximize

the probability of waiting less than 10 minutes for the ferry?

42. Delicious Candy markets a two-pound box of assorted chocolates. Because of

imperfections in the candy making equipment, the actual weight of the chocolate has a

uniform distribution ranging from 31.8 to 32.6 ounces.

a. Define a probability density function for the weight of the box of chocolate.

b. What is the probability that a box weighs (1) exactly 32 ounces; (2) more than

32.3 ounces; (3) less than 31.8 ounces?

c. The government requires that at least 60% of all products sold weigh at least as

much as the stated weight. Is Delicious violating government regulations?

43. The time at which the mailman delivers the mail to Ace Bike Shop follows a normal

distribution with mean 2:00 PM and standard deviation of 15 minutes.

a. What is the probability the mail will arrive after 2:30 PM?

b. What is the probability the mail will arrive before 1:36 PM?

c. What is the probability the mail will arrive between 1:48 PM and 2:09 PM?

44. The township of Middleton sets the speed limit on its roads by conducting a traffic study

and determining the speed (to the nearest 5 miles per hour) at which 80% of the drivers

travel at or below. A study was done on Brown's Dock Road that indicated driver's

speeds follow a normal distribution with a mean of 36.25 miles per hour and a variance

of 6.25.

a. What should the speed limit be?

b. What percent of the drivers travel below that speed?

45. A light bulb manufacturer claims its light bulbs will last 500 hours on the average. The

lifetime of a light bulb is assumed to follow an exponential distribution.

a. What is the probability that the light bulb will have to be replaced within 500

hours?

b. What is the probability that the light bulb will last more than 1000 hours?

c. What is the probability that the light bulb will last between 200 and 800 hours.

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