Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0μ=74.0 beats per minute and a standard deviation of sigma equals 12.5σ=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 between 70 beats per minute and 78 beats per minute.

Answer 1

Here the mean is 74 and s.d is 12,5.

For x being pulse rate of a randomly selected female. We need to find

P[70

To calculate this we convert x to z the standard normal distribution along with its ranges by subtrating with mean and then dividing by sd.

z=(x-mean)/sd

P[(70-74)/12.5

P[ -0.32

From the standard normal distribution table P[z<0.32]=0.62552.

You can find these values by looking up the standard normal table and checking value across z=0.32 and z=-0.32

P[z<-0.32]=0.37448

Hence required probability= 0.62552-0.37448

=0.25104 is the probability that pulse rate is between 70 and 78 beats per minute.