Question

In the EAI sampling problem, the population mean is 51,600 and the population standard deviation is 5,000. When the sample size is n=30, there is a 0.4176 probability of obtaining a sample mean within +/- 500 of the population mean.

1. What is the probability that the sample mean is within 500 of the population mean if a sample of size 60 is used (to 4 decimals)?

2. What is the probability that the sample mean is within 500 of the population mean if a sample of size 120 is used (to 4 decimals)?

Answer 1

Solution :

Given that,

mean = = 51600

standard deviation = = 5000

1) n = 60

= = 51600

= / n = 5000 / 60 = 645.50

P(51100 < < 52100)  

= P[(51100 - 51600) /645.50 < ( - ) / < (52100 - 51600) / 645.50)]

= P(-0.77 < Z < 0.77)

= P(Z < 0.77) - P(Z < -0.77)

Using z table,  

= 0.7794 - 0.2206

= 0.5588

2) n = 120

= = 51600

= / n = 5000 / 120 = 456.44

P(51100 < < 52100)  

= P[(51100 - 51600) /456.44 < ( - ) / < (52100 - 51600) / 456.44)]

= P(-1.10 < Z < 1.10)

= P(Z < 1.10) - P(Z < -1.10)

Using z table,  

= 0.8643 - 0.1357

= 0.7286