Question

The 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 greater than 3.76 inches?

Answer 1

Answer: 0.0643

Step-by-step explanation:

Given :  The diameters of red delicious apples of an orchard have a normal distribution with

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

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

The formula for z -score :

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

For x= 3.76 inches ,

$z=\dfrac{3.76-3}{0.5}=1.52$

The p-value = $P(z>1.52)=1-P(z$

$=1-0.9357445=0.0642555\approx0.0643$

Hence, the probability of picking an apple with diameter greater than 3.76 inches = 0.0643.