Question

A population has a mean of 300 and a standard deviation of 90. Suppose a sample of size 100 is selected and x is used to estimate μ.

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

b. What is the probability that the sample mean will be within +/- 14 of the population mean (to 4 decimals)?

Answer 1

We use the formula:
`z = (x-\mu)/((\sigma)/( √(n))) = (x-\mu)/((90)/(√(100))) = (x-\mu)/(9)`
a.
`z = (5)/(9) = 0.56`, so we then find P(-0.56 < z < 0.56) from z-tables, and this is equivalent to 0.4246.
b.
`z = (14)/(9) = 1.56`, so we find P(-1.56 < z < 1.56) from z-tables, and this value is equivalent to 0.8812.