Question

The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.

Find the probability that the sum of the 40 values is greater than 7,450. (Round your answer to four decimal places.)

Answer 1

Solution :

mean = = 180

standard deviation = = 20

n = 40

= = 180

= / n = 20/ 40 = 3.16

sample average = = 7450 / 40 = 186.25

P( > 186.25) = 1 - P( < 186.25)

= 1 - P[( - ) / < (186.25 - 180) / 3.16 ]

= 1 - P(z < 1.98)

Using z table,    

= 1 - 0.9761

= 0.0239