MATH SOLVE

9 months ago

Q:
# The lengths of pregnancies are normally distributed with a mean of 264 days and a standard deviation of 15 days. if 36 women are randomly selected, find the probability that they have a mean pregnancy between 264 days and 266 days.

Accepted Solution

A:

Given that a sample of 36 women is selected, the probability that the mean is between 264 days and 266 days will be found as follows:

the std deviation of the sample will be:

Ο/βn

plugging the values we obtain:

15/β36

=15/6

=2.5

hence the z-score when x=264 will be:

z=(264-264)/2.5

z=0

thus:

P(x<264)=P(z<0)=0.5

the z-score when x=266 will be:

z=(266-264)/2.5

z=0.8

hence

P(x<266)=P(z<0.8)=0.7881

thus

P(264<x<266)=P(0.5<z<0.7881)

=0.7881-0.5

=0.2881

Answer: 0.2881

the std deviation of the sample will be:

Ο/βn

plugging the values we obtain:

15/β36

=15/6

=2.5

hence the z-score when x=264 will be:

z=(264-264)/2.5

z=0

thus:

P(x<264)=P(z<0)=0.5

the z-score when x=266 will be:

z=(266-264)/2.5

z=0.8

hence

P(x<266)=P(z<0.8)=0.7881

thus

P(264<x<266)=P(0.5<z<0.7881)

=0.7881-0.5

=0.2881

Answer: 0.2881