Q-19.
A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size
100 is selected and x is used to estimate m.
a. What is the probability that the sample mean will be within ±5 of the population mean?
b. What is the probability that the sample mean will be within ±10 of the population mean?
Soln:
a) Here is the samle mean. Then is normally distributed with mean 200
and standard deviation = = 5
Therefore follows a standard normal distribution.
Now the probability that sample mean will be within 5 of the population mean is given by
P[195 < < 205 ]
= 0.6827
(b) the probabity that sample mean will be within 10 of the population mean is given by
P[190 < < 210 ]