Question

The mean incubation time of fertilized eggs is

21

days. Suppose the incubation times are approximately normally distributed with a standard deviation of

11

day.

​(a) Determine the

13th

percentile for incubation times.

​(b) Determine the incubation times that make up the middle

95​%.

Answer 1

/* NOTE: CHECK STANDARD DEVIATION IS 11 I USED IT AS 11 AS MENTION IN QUESTION OTHERWISE CHANGE IT'S VALUE IN BELOW EQUATION YOU WILL GET ANSWER FOR DESIRED SD */

Ans a) The 13^th percentile for incubation times is 8.57

Explanation:

Mean:

Standard deviation:

Formula to calculate z-score:

we are given:

Using Excel function:=NORM.S.INV(0.13) we get z = -1.13

Therefore,

ans.

Therefore,

The 13^th percentile for incubation times is 8.57

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Ans b) ( -0.56 TO  42.56 ) incubation times make up the middle 95%

Explanation

To find the middle 95​%.

The bottom percent is: (1-0.95)/2 = 0.025

Now, using excel function:=NORM.S.INV(0.025) the z-score is -1.96 so, using symmetry the other z-score is 1.96

Both values of X using formula X = z +

Thus,

-0.56-42.56 days make up the middle 95%

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