Question

A population has a mean of 400 and a standard deviation of 70. Suppose a sample of size 125 is selected. Use z-table.

a. What is the probability that the sample mean will be within +4 or -4 of the population mean (to 4 decimals)?

b. What is the probability that the sample mean will be within +10 0r -10 of the population mean (to 4 decimals)?

Answer 1

Solution :

Given that,

mean = = 400

standard deviation = = 70

n = 125

= 400

= / n = 70 / 125 = 6.26099

(a)

P(396 < < 404) = P((396 - 400) / 6.26099 <( - ) / < (404 - 400) / 6.026099))

= P(-0.64 < Z < 0.64)

= P(Z < 0.64) - P(Z < -0.64) Using z table,

= 0.7389 - 0.2611

= 0.4778

Probability = 0.4778

(b)

P(390 < < 410) = P((390 - 400) / 6.26099 <( - ) / < (410 - 400) / 6.026099))

= P(-1.60 < Z < 1.60)

= P(Z < 1.60) - P(Z < -1.60) Using z table,

= 0.9452 - 0.0548

= 0.8904

Probability = 0.8904