Question

A population has a mean of 300 and a standard deviation of 70. Suppose a sample of size 125 is selected and  is used to estimate . Use z-table.

1. What is the probability that the sample mean will be within +/- 3 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)
   
   
2. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

Answer 1

Answer :

Given that :

Mean = = 300

Standard deviation = = 70

Sample size n = 125

a)Given data is,

within population mean +/- 3

therefore,

----------> (1)

First consider, is :

therefore,

Now,consider

therefore,

Substitute these two values in equation 1,

b)Given data is,

within population mean +/- 10

therefore,

----------> (1)

First consider, is :

therefore,

Now,consider

therefore,

Substitute these two values in equation 1,