Question

In the EAI sampling problem, the population mean is $51,200 and the population standard deviation is $5,000. When the sample size is n = 20, there is a 0.3453 probability of obtaining a sample mean within +/- $500 of the population mean. Use z-table. What is the probability that the sample mean is within $500 of the population mean if a sample of size 40 is used (to 4 decimals)? What is the probability that the sample mean is within $500 of the population mean if a sample of size 80 is used (to 4 decimals) ReplyForward

Answer 1

Solution :

a.

= / n = 5000 / 40 = 790.5694

= P[(-500) / 790.5694 < ( - ) / < (500) / 790.5694)]

= P(-0.63 < Z < 0.63)

= P(Z < 0.63) - P(Z < -0.63)

= 0.7357 - 0.2643

= 0.4714

Probability = 0.4714

b.

= / n = 5000 / 80 = 559.0170

= P[(-500) / 559.0170 < ( - ) / < (500) / 559.0170)]

= P(-0.89 < Z < 0.89)

= P(Z < 0.89) - P(Z < -0.89)

= 0.8133 - 0.1867

= 0.6266

Probability = 0.6266