Question

In the EAI sampling problem, the population mean is $51,400 and the population standard deviation is $5,000. When the sample size is n = 30, there is a 0.489 probability of obtaining a sample mean within +/- $600 of the population mean. Use z-table.

a. What is the probability that the sample mean is within $600 of the population mean if a sample of size 60 is used (to 4 decimals)?

b. What is the probability that the sample mean is within $600 of the population mean if a sample of size 120 is used (to 4 decimals)?

Answer 1

Solution :

Given that,

mean = = 51400

standard deviation = = 5000

a) n = 60

=   = 51400

= / n = 5000 / 60 = 645.5

P(50800 < < 52000)  

= P[(50800 - 51400) /645.5 < ( - ) / < (52000 - 51400) /645.5 )]

= P( -0.93 < Z < 0.93)

= P(Z < 0.93) - P(Z < -0.93)

Using z table,  

= 0.8238 - 0.1762  

= 0.6476

b) n = 120

=   = 51400

= / n = 5000 / 120 = 456.4

P(50800 < < 52000)  

= P[(50800 - 51400) /456.4 < ( - ) / < (52000 - 51400) /456.4 )]

= P( -1.31 < Z < 1.31)

= P(Z < 1.31) - P(Z < -1.31)

Using z table,  

= 0.9049 - 0.0951

= 0.8098