The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days.a. Find the probability of a pregnancy lasting307days or longer.b. If the length of pregnancy is in the lowest33​%,then the baby is premature.Find the length that separates premature babies from those who are not premature

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Asked Nov 7, 2019
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The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days.

a. Find the probability of a pregnancy lasting307days or longer.

b. If the length of pregnancy is in the lowest33​%,then the baby is premature.

Find the length that separates premature babies from those who are not premature

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Expert Answer

Step 1

From the given information,

Let x be random variable that represents the lengths of pregnancies which follows normal distribution with mean days of 266 and standard deviation of 15 days.

Thus,

 

Step 2

a)

The probability that the pregnancy lasting 307 days is-

P(X2 307) 1-P(X < 307)
X-307-266
1- P
15
1-P(Z <2.73)
=1-0.996
0.004
help_outline

Image Transcriptionclose

P(X2 307) 1-P(X < 307) X-307-266 1- P 15 1-P(Z <2.73) =1-0.996 0.004

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Step 3

b)

Here, it is required to calculate length of premature baby to mature for tha...

P(X <x) 0.33
X-
P
x-266
=0.33
15
x -266
(0.33)
15
x -266
=-0.439[using standard normal table]
15
x 259.401
help_outline

Image Transcriptionclose

P(X <x) 0.33 X- P x-266 =0.33 15 x -266 (0.33) 15 x -266 =-0.439[using standard normal table] 15 x 259.401

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