SOMEONE PLEAS HELLPPP !! The diameters of Breaburn apples are normally distributed with a mean of 8.2cm and a standard deviation of 2.8cm. If you had a shipment of 2000 apples, how many apples would have a diameter: a) smaller than 5.9cm? b) larger than 10.2cm?

a. 412

b. 478

Step-by-step explanation:

We have to find the corresponding probabilities using the standard normal table, that is, we must calculate the value of z, the formula of z is as follows:

z = (x - m) / sd

where x is the value to evaluate, m is the mean and sd is the standard deviation.

We are told that the mean is 8.2 cm and the standard deviation is equal to 2.8 cm.

a. smaller than 5.9cm?

In this case x would be 5.9, we replace and we are left with:

z = (x - m) / sd

z = (5.9 - 8.2) /2.8

z = -0.82

If we look for this value in the normal table (attached) it corresponds to 0.2061, to know the number of apples we must multiply this value by the total value of apples, that is 2000. Therefore:

2000 * 0.2061 = 412.2 = 412

b) larger than 10.2cm?

In this case x would be 10.2, we replace and we are left with:

z = (x - m) / sd

z = (10.2 - 8.2) /2.8

z = 0.71

In this case z corresponds to 0.7611, but since this is the value is smaller than 10.2, and we need is larger than 10.2cm, it would be the complement, that is:

1 - 0.7611 = 0.2389

Now to calculate the total number of apples we have:

2000 * 0.2389 = 477.8 = 478

b

step-by-step explanation:

x+14

step-by-step explanation: