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 81 beats per minute.

b. If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 81

beats per minute.

Answer 1

Solution :

Given that ,

mean = = 74

standard deviation = = 12.5

a) P(x < 81) = P[(x - ) / < (81-74) /12.5 ]

= P(z < 0.56)

= 0.7123

Probability = 0.7123

b)

n = 25

=   = 74

= / n = 12.5/ 25 = 2.5

P( <81 ) = P(( - ) / < (81-74) /2.5 )

= P(z < 2.8)

= 0.9974

probability= 0.9974