Question

1. A normally distributed population has a mean of 69 and a standard deviation of 13. Sample averages from samples of size 24 are collected. What would be the lower end of the centered interval that contains 95% of all possible sample averages?

Round to the nearest hundredth

2. Suppose a sample of 104 healthy children is taken from a population with a standard deviation of 0.4 degrees Fahrenheit. What would be sigma x-bar?

Round to the nearest thousandth

Answer 1

solution:

Given that,

mean = = 69

standard deviation = =13

n = 24

= 69

= / n = 13/24=2.65

Using standard normal table,

P(Z < z) = 95%

= P(Z < z) = 0.95  

= P(Z <1.65 ) = 0.95

z = 1.65 Using standard normal table,

Using z-score formula  

= z * +   

= 1.65*2.65+69

= 73.37

part2

sampling distribution of standard deviation

=  / n = 0.4/ 104=0.039

= 0.039