Incy length The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 270 days and a standard deviation of 9

days

(a) What is the minimum pregnancy length that can be in the top 12% of pregnancy lengths?

(b) What is the maximum pregnancy length that can be in the bottom 6% of pregnancy lengths?

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(a) The minimum pregnancy length is days

(Round to one decimal place as needed)

(b) The maximum pregnancy length is days.

(Round to one decimal place as needed)

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Enter your answer in each of the answer boxes

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(a) 259.5 days

(b) 284 days

Step-by-step explanation:

Let X represent the pregnancy length in days.

It is provided that .

(a)

Let a represent the minimum pregnancy length that can be in the top 12% of pregnancy lengths.

Then,

P (X < a) = 0.12

⇒ P (Z < z) = 0.12

The corresponding z-score is, z = -1.17.

*Use a z-table.

Compute the value of x as follows:

Thus, the minimum pregnancy length that can be in the top 12% of pregnancy lengths is 259.5 days.

(b)

Let b be the maximum pregnancy length that can be in the bottom 6% of pregnancy lengths.

Then,

P (X > b) = 0.06

⇒ P (X < b) = 0.94

⇒ P (Z < z) = 0.94

The corresponding z-score is, z = 1.56.

*Use a z-table.

Compute the value of x as follows:

Thus, the maximum pregnancy length that can be in the bottom 6% of pregnancy lengths is 284 days.

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