Applied Statistics and Probability for Engineers, 7th edition 2017
3-12
3.6.14 Let X denote the number of customers who visit the website to obtain the first order.
3.6.15 X = the number of defective bulbs in an array of 30 LED bulbs. Here X is a binomial random variable with p = 0.001
and n = 30
Section 3-7
3.7.1 X has a hypergeometric distribution with N = 100, n = 4, K = 20
( )( )
20 80
13
20(82160)
3.7.2 Here N = 10, n = 3, K= 4
Applied Statistics and Probability for Engineers, 7th edition 2017
3-13
3.7.3 Let X denote the number of men who carry the marker on the male chromosome for an increased risk for high blood
pressure. Here N = 800, K = 240
3.7.4 Let X denote the number of cards in the sample that are defective.
a)
= − =
( 1) 1 ( 0)
P X P X
b)
= − =
( 1) 1 ( 0)
P X P X
3.7.5 N = 300
3.7.6 Let X denote the count of the numbers in the state’s sample that match those in the player’s sample.
Then, X has a hypergeometric distribution with N = 40, n = 6, and K = 6.
Applied Statistics and Probability for Engineers, 7th edition 2017
3-14
3.7.7 Let X denote the number of blades in the sample that are dull.
a)
= − =
( 1) 1 ( 0)
P X P X
3.7.8 a) Assuming X has a binomial distribution with n = 4 and p = 0.2
b) X is approximately binomially distributed with n = 20 and p = 20/140 = 1/7.
( )
= − = = = − =
0 20
20
0
16
( 1) 1 ( 0) 1 0.0458 0.9542
77
P X P X
3.7.9 Let X denote the number of patients in the sample that adhere. Here X has a hypergeometric distribution with
N = 500, K = 50 and n = 20 when the sample size is 20.
−
50 500 50
Applied Statistics and Probability for Engineers, 7th edition 2017
3-15
b)
= = + =( 2) ( 0) ( 1)P X P X P X
3.7.10 Let X = the number of major customers that accept the plan in the sample. Here X has hypergeometric distribution with
N = 50, K = 15, and n = 10 when the sample size is 10.
3.7.11 Let X = the number of sites with lesions in the sample. Here X has hypergeometric distribution with N = 50,
K = 5 and n = 8 when the sample size is 8.
Applied Statistics and Probability for Engineers, 7th edition 2017
3-16
Section 3-8
3.8.2 a) Let X denote the number of calls in one hour. Then, X is a Poisson random variable with
= 10.
−
= = =
10 5
10
( 5) 0.0378
e
PX
.
−
3.8.4 a)
= 14.4, P(X = 0) = 6E10−7
3.8.5
= 1, Poisson distribution. f(x) = e− x/x!
Applied Statistics and Probability for Engineers, 7th edition 2017
3-17
3.8.7 a)
= 0.61 and P(X ≥ 1) = 0.4566
3.8.9 a) Let X denote the number of flaws in 10 square feet of plastic panel.
3.8.10 a) Let X denote the number of inclusions in cast iron with a volume of cubic millimeter.
Applied Statistics and Probability for Engineers, 7th edition 2017
3-18
3.8.11 a) Let X denote the number of cabs that pass your workplace in 10 minutes.
b) Let Y denote the number of cabs that pass your workplace in 20 minutes.
3.8.12 a) Let X denote the number of visits in a day.
c) Let Z denote the number of visits in T days that satisfies the given condition.
Supplemental Exercises
Applied Statistics and Probability for Engineers, 7th edition 2017
3-19
3.S17 Let X denote the number of mornings needed to obtain a green light.
Then X is a geometric random variable with p = 0.20.
3.S18 Geometric random variable with p = 0.1
3.S19 Let X denote the number of fills needed to detect three underweight packages.
Then, X is a negative binomial random variable with p = 0.001 and r = 3.
3.S20 Let X denote the number of totes in the sample that do not conform to purity requirements. Then, X has a
hypergeometric distribution with N = 15, n = 3, and K = 2.
Applied Statistics and Probability for Engineers, 7th edition 2017
3-20
3.S22 a) Let X denote the number of messages sent in one hour.
3.S23 Let X denote the number of calls that are answered in 30 seconds or less.
Then, X is a binomial random variable with p = 0.75.
3.S24 X Poisson with E(X) = 0.01(100) = 1
3.S25 Let X denote the number of individuals that recover in one week. Assume the individuals are independent.
3.S26 a) P(X = 1) = 0, P(X = 2) = 0.0025, P(X = 3) = 0.01, P(X = 4) = 0.03, P(X = 5) = 0.065
3.S27 Let X denote the number of assemblies needed to obtain 5 defectives.
3.S28 Let X denote the number of products that fail during the warranty period. Assume the units are independent. Then,
X is a binomial random variable with n = 500 and p = 0.02.
Applied Statistics and Probability for Engineers, 7th edition 2017
3-21
3.S29
3.S31 Let X denote the number of errors in a sector. Then, X is a Poisson random variable with E(X) = 0.32768.
3.S32 Let X and Y denote the number of bolts in the sample from supplier 1 and 2, respectively.
3.S33 a) Hypergeometric random variable with N = 500, n = 5, and K = 125.
Applied Statistics and Probability for Engineers, 7th edition 2017
3-22
3.S34 Let X denote the number of orders placed in a week in a city of 800,000 people.
3.S35 a) Let X denote the number of cacti per 10,000 square meters.
3.S36 Let X denote the number of totes in the sample that exceed the moisture content.