Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts (a) through (c) below. 

a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute. .6255 

b. If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 78 beats per minute. 

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Answer 1

Solution :

Given that ,

mean = μ = 74.0

standard deviation = σ = 12.5

n = 1

μx̅= 74.0

σx̅=σ  /√n =12.5 / √1=12.5

P(x̅- μx̅) / σx̅

= P(z

Using z table  

= 0.6255

probability=0.6255

(b)

n = 16

μx̅= 74.0

σx̅=σ  /√n =12.5 / √16=3.125

P(x̅- μx̅) / σx̅

= P(z

Using z table  

= 0.8997

probability=0.8997

normal distribution use for any sample size