Question

Suppose that the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1 month. 19 randomly selected people were asked what age they learned to walk. Round all answers to two decimal places. A. xBar~ AND( , ) B. For the 19 people, find the probability that the average age that they learned to walk is between 11.5 and 12.5 months old. C. What is the probability that one randomly selected person learned to walk when they were between 11.5 and 12.5 months old

Answer 1

Answer with explanation:

Given : The age that children learn to walk is normally distributed with $\mu=12\text{ months}$ and $\sigma=1\text{ month}$.

Let x be the age that children learn to walk  .

B) Using formula $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

n= 19

For x= 11.5

$z=\dfrac{11.5-12}{\dfrac{1}{\sqrt{19}}}=-2.18$

For x= 12.5

$z=\dfrac{12.5-12}{\dfrac{1}{\sqrt{19}}}=2.18$

Then, by using the z-value table , for the 19 people, the probability that the average age that they learned to walk is between 11.5 and 12.5 months old will be :-

$P(-2.18$

Hence, for the 19 people, the probability that the average age that they learned to walk is between 11.5 and 12.5 months old = 0.9707

C. Using formula $z=\dfrac{x-\mu}{\sigma}$

For x= 11.5

$z=\dfrac{11.5-12}{1}=-0.5$

For x= 12.5

$z=\dfrac{12.5-12}{1}=0.5$

Then, by using the z-value table , the probability that the average age that they learned to walk is between 11.5 and 12.5 months old will be :-

$P(-0.5$

Hence, the probability that the average age that they learned to walk is between 11.5 and 12.5 months old = 0.3829