(8 points) The probability that the total length of pregnancy for 15 randomly selected women is greater than a certain amount is 0.05. Find this total length.

The total length to be calculated = 290.32 days

Step-by-step explanation:

The probability that the total length of pregnancy for 15 randomly selected women is greater than a certain amount is 0.05.

Let the standardized score of this certain amount be z',

P(z>z') = 0.05

But on the normal distribution tables, what we have is P(z≤(any random z-score)

So, expressing P(z>z') in that form,

Mathematically,

P(z>z') = 1 - P(z≤z')

0.05 = 1 - P(z≤z')

P(z≤z') = 1 - 0.05 = 0.95

From the normal distribution table, z' = 1.645

The z-score formula is

z = (x - xbar)/σ

Where z = 1.645

xbar = mean = 264 days

σ = standard deviation = 16 days

x = number of days that corresponds to the z-score of 1.645 = ?

1.645 = (x - 264)/16

x = 26.32 + 264 = 290.32 days.

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