Question

The lenghts of a particular animal's pregnancies are approximately normally distributed, with mean u= 274 days and standard deviation o = 20 days.

(A) What proportion of pregnancies lasts more thatn 309 days?

(B) What proportion of pregnancies lasts between 249 and 279 days?

(C) Determine the 11th percentile for pregnancies times.

(D) Determine the pregnancies times that make up the middle 89.9%

Answer 1

Let X is a random variable shows the length of pregnancies. Here X has normal distribution with parameters as follows:

(a)

The z-score for X = 309 is

The required proportion, using z table, is

(b)

The z-score for X = 249 is

The z-score for X = 279 is

The required proportion, using z table, is

(c)

Here we need z-score that has 0.11 area to its left. The z-score -1.23 has approximately 0.11 area to its left. The required X is:

(c)

The area at both tails is;

Here we need z-score that has 0.0505 area to its left. The z-score -1.64 has approximately 0.0505 area to its left. The required lower limit is:

Here we need z-score that has 0.0505 area to its right. By symmetry, the z-score 1.64 has approximately 0.0505 area to its right. The required upper limit is:

The required interval is (241.20, 306.80).