Mathematics: The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 264 days and a standard deviation of 10 days. a) what is the minimum pregnancy length that can be in the top 9% of pregnancy lengths? b) what is the maximum pregnancy length that can be in the bottom 7% of pregnancy lengths?

3:45 pmStep-by-step explanation:If it takes 30 minutes to get there and 30 minutes to be early. Minus 1 hour from 4:45 pm and you get 3:45 pm...

The pregnancy length in days for a population of

arianaw6735

08.01.2022

Approximately 278 is the minimum pregnancy length that can be in the top 9% of pregnancy lengths.

approximately 279 is the minimum pregnancy length that can be in the top 7% of pregnancy lengths.

Step-by-step explanation:

We are given the following information:

Mean, μ = 264 days

Standard Deviation, σ = 10 days

We are given that the distribution of pregnancy length in days is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(X>x) = 9% = 0.09

We have to find the value of x such that the probability is 0.09.

P(X > x)

$P( X x) = P( z \displaystyle\frac{x - 264}{10})=0.09$

$= 1 -P( z \leq \displaystyle\frac{x - 264}{10})=0.09$

$P( z \leq \displaystyle\frac{x - 264}{10})=1-0.09=0.91$

Calculation the value from standard normal z table, we have,

$P(z \leq 1.341) = 0.91$

$\displaystyle\frac{x - 264}{10} = 1.341\\x = 277.41$

Hence, approximately 278 is the minimum pregnancy length that can be in the top 9% of pregnancy lengths.

b) P(X>x) = 7% = 0.07

We have to find the value of x such that the probability is 0.07.

P(X > x)

$P( X x) = P( z \displaystyle\frac{x - 264}{10})=0.07$

$= 1 -P( z \leq \displaystyle\frac{x - 264}{10})=0.07$

$P( z \leq \displaystyle\frac{x - 264}{10})=1-0.07=0.93$

Calculation the value from standard normal z table, we have,

$P(z \leq 1.476) = 0.93$

$\displaystyle\frac{x - 264}{10} = 1.476\\x = 278.76$

Hence, approximately 279 is the minimum pregnancy length that can be in the top 7% of pregnancy lengths.

0,0(0 оценок)