Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 76.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 83 beats per minute.

Answer 1

Solution: We are given that females have pulse rates that are normally distributed with a
`\mu=76,\sigma=12.5`

We have to find
`P(\bar{x}<83)`

First we need to determine the z score corresponding to
`\bar{x}=83`

We know that:

`z=\frac{\bar{x}-\mu}{(\sigma)/(√(n))   }`

`=(83-76)/((12.5)/(√(4)))`

`=1.12`

Now, we have to find
`P(z<1.12)`

Using the standard normal table, we have:

`P(z<1.12)=0.8686`

Therefore, if 4 adult females are randomly selected the probability that they have pulse rates with a mean less than 83 beats per minute is 0.8686