Question

Answer the follow questions utilizing MS Excel and the following functions: =norm.dist(), =norm.inv(), =t.dist(), =t.dist.rt(), and/or =t.inv()

Assume that adult women have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute.

Part 1:
If 1 adult woman is randomly​ selected, find the probability that her pulse rate is between 68 beats per minute and 80 beats per minute.
The probability is 36.88%. correct
​(Round answer to nearest hundredth of a percent - i.e. 23.34%)

Part 2:
If 16 adult women are randomly​ selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 80 beats per minute.
The probability is ______?______
​(Round answer to nearest hundredth of a percent - i.e. 23.34%

Answer 1

Since adult women have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute.

Part 1. To find the probability between 68<X<80 we need to find Z score at both X as

and at X=80

So, P(68<X<80)=P(-0.48<Z<0.48)

=P(Z<0.48)-P(Z<-0.48)

The respective probability is calculated using the Z score table or by excel tool formula =NORM.DIST(80,74,12.5,TRUE)-NORM.DIST(68,74,12.5,TRUE)

=0.3688

=36.88%

Part2. If 16 adult women are randomly selected,

The probability that they have pulse rates with a mean between 68 beats per minute and 80 beats per minute.

Since n=16 which is less than 30 hence t distribution is applicable here as

at X=68

and at X=80

Using Excel formula as

=T.DIST(1.92,15,TRUE)-T.DIST(-1.92,15,TRUE)

=0.9259

=92.59%