DON'T GOT MUCH TIME PLEASEEE HELP ME OUT! BEINLIEST 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 must calculate the value of z from the following:

z = (x - m) / sd

where x is the value to evaluate, m is the mean that is equal to 8.2 cm and sd is the standard deviation that is equal to 2.8 cm.

a. x <5.9

p (z <(x - m) / sd)

z = (x - m) / sd

z = (5.9 - 8.2) /2.8

z = -0.82

p (z <-0.82)

In the normal table (attached) 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) x> 10.2

p (z <(x - m) / sd)

z = (x - m) / sd

z = (10.2 - 8.2) /2.8

z = 0.71

p (z> -0.71) = 1 - p (z <-0.71)

p (z> -0.71) = 1 - 0.7611 = 0.2389

Therefore the number of apples would be:

2000 * 0.2389 = 477.8 = 478