Question

Assume that females have pulse rates that are normally distributed with a mean of μ=74.0beats per minute and a standard deviation of 5σ=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 80 beats per minute.

b) If 44 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 80 beats per minute.

Answer 1

Solution :

Given that ,

mean =   = 74.0

standard deviation = = 12.5

(A)n = 1

= 74.0

=  / n = 12.5 / 1=12.5

P( < 80) = P[( - ) / < (80 -74.0) / 12.5]

= P(z <0.48 )

Using z table  

= 0.6844   

probability= 0.6844   

(B)

n =44

= 74.0

=  / n = 12.5 / 44=1.8845

P( < 80) = P[( - ) / < (80 -74.0) / 1.8845]

= P(z <3.18 )

Using z table  

= 0.9993

probability= 0.9993