Question

A Canadian study examined the pregnancy weight gain of underweight mothers, women who had been underweight before becoming pregnant. A Normal distribution with mean 36.6 lb and standard deviation 11.9 lb is a reasonable model for the distribution of pregnancy weight gains in this population.

a) Perform the appropriate computation and fill in the blank to complete this sentence in context: In this population, the first quartile of pregnancy weight gains is_____.
b) For underweight mothers, health organizations recommend a pregnancy weight gain between 27.5 lb and 39.5 lb. What is the probability that a randomly selected underweight mother in Canada would have a pregnancy weight gain in the recommended range?

Answer 1

The correct answer is:

(a) 44.6 lb

(b) 0.371

Explanation:

Given values are:

Mean,

`\mu=36.6`

Standard deviation,

`\sigma=11.9`

(a)

The z distance third quartile will be:

⇒
`P(Z<0.674)=0.75`

`z =0.674`

By using the z-score formula, we get

⇒
`x=z* \sigma+ \mu`

`=0.674* 11.9+36.6`

`=44.62`

(b)

⇒
`P(27.5<x<39.5) = P[{((27.5-36.6))/(11.9) <((x-\mu))/(\sigma) <((39.5-36.6))/(11.9) }]`

`=P(-0.76<z<0.24)`

`=P(z<0.24)-P(z<-0.76)`

By using the z table, we get

`=0.5948-0.2236`

`=0.371`