Question

he diameters of red delicious apples of an orchard have a normal distribution with a mean of 3 inches and a standard deviation of 0.5 inch. One apple will be randomly chosen. What is the probability of picking an apple with diameter between 2.5 and 4.25 inches?

Answer 1

Answer: 0.8351

Step-by-step explanation:

Given :Mean : $\mu=\text{ 3 inches}$

Standard deviation : $\sigma =\text{ 0.5 inch}$

The formula for z -score :

$z=\dfrac{x-\mu}{\sigma}$

For x= 2.5 ,

$z=\dfrac{2.5-3}{0.5}=-1$

For x= 4.25 ,

$z=\dfrac{4.25-3}{0.5}=2.5$

The p-value = $P(-1$

$=0.9937903-0.1586553=0.835135\approx0.8351$

Hence,  the probability of picking an apple with diameter between 2.5 and 4.25 inches =0.8351.