Answer:
C. 97.5%
Step-by-step explanation:
For identify the percent of the onions that will be accepted by the grocery, we need to standardized the minimum diameter accepted.
Standardized is to find the equivalent number of 2.75 in a normal distribution with mean 0 and standard deviation 1. This is calculate as:
\(Z=\frac{2.75-3.25}{0.25}=-2\)
Where z is the equivalent value of 2.75 in the standard normal distribution, 3.25 is the mean and 0.25 is the standard deviation.
So, 2.75 in a normal distribution with mean 3.25 and standard deviation of 0.25 is equivalent to have a -2 in standard normal distribution.
A standard normal distribution is a normal distribution with mean 0 and standard deviation 1.
Finally the percent of the onions that will be accepted by the grocery store is calculate as the probability of z to be bigger that -2 in a standard normal distribution. That is:
P(Z>-2)=0.9772
This value can be found in a table of standard normal distribution that given a z, it show you the area on the right of this number.
So, the percent of onions that are going to be accepted is approximately 97.5%
