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?

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Cricetus Cricetus · Answer 1 · 2021-06-13T09:40:40+02:00

Answer:

The correct answer is:

(a) 44.6 lb

(b) 0.371

Step-by-step explanation:

Given values are:

Mean,

[tex]\mu=36.6[/tex]

Standard deviation,

[tex]\sigma=11.9[/tex]

(a)

The z distance third quartile will be:

⇒ [tex]P(Z<0.674)=0.75[/tex]

[tex]z =0.674[/tex]

By using the z-score formula, we get

⇒ [tex]x=z\times \sigma+ \mu[/tex]

[tex]=0.674\times 11.9+36.6[/tex]

[tex]=44.62[/tex]

(b)

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

[tex]=P(-0.76<z<0.24)[/tex]

[tex]=P(z<0.24)-P(z<-0.76)[/tex]

By using the z table, we get

[tex]=0.5948-0.2236[/tex]

[tex]=0.371[/tex]