Question

the length of a particular animals pregnancies are approximately normally distributed with a mean u=252 days and standard deviation o=12 days

a. what proportion of pregnacies last more than 267 days?

b. what proportion of pregnancies lasts between 234 and 255 days?

c. what is the probabilty that a randomly selected pregancy lasts no more than 237 days?

d. a "very preterm" baby is one whose gestation period is less than 222 days. Are very preterm babies unusual?

Answer 1

Given = 252, 12

To find the probability, we need to find the z scores.

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(a) For P( X < 267)

Z = (267 – 252)/12 = 1.25

The required probability from the normal distribution tables is = 0.8944

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(b) For P (234 < X < 255) = P(X < 255) – P(X < 234)

For P( X < 255)

(255 – 252)/12 = 0.25

The probability for P(X < 255) from the normal distribution tables is = 0.5987

For P( X < 234)

(234 – 252)/12 = -1.5

The probability for P(X < 234) from the normal distribution tables is = 0.0668

Therefore the required probability is 0.5987 – 0.0668 = 0.5319

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(c) P(No more than 237) = P(X 237) = P(X < 237)

Z = (237 – 252)/12 = -1.25

The required probability from the normal distribution tables is = 0.1056

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(d) P(X < 222)

Z = (222 – 252)/12 = -2.5

The required probability from the normal distribution tables is = 0.0062

Yes, pretern babies are very unusual as the percentage of such babies is < 5% (0.62%)

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