the diameters of cherry tomatoes produced by a large farm have an approximately normal distribution, with a…

the diameters of cherry tomatoes produced by a large farm have an approximately normal distribution, with a mean diameter of 22 mm and a standard deviation of 2.5 mm. after they are picked and washed, tomatoes with a diameter of at most 15 mm or at least 30 mm are rejected and not sold. what proportion of such tomatoes are rejected? find the z - table here. 0.0033 0.0201 0.9799 0.9967

the diameters of cherry tomatoes produced by a large farm have an approximately normal distribution, with a mean diameter of 22 mm and a standard deviation of 2.5 mm. after they are picked and washed, tomatoes with a diameter of at most 15 mm or at least 30 mm are rejected and not sold. what proportion of such tomatoes are rejected? find the z - table here. 0.0033 0.0201 0.9799 0.9967

Answer

Answer:

A. 0.0033

Explanation:

Step1: Calculate z - scores

For $x = 15$, $z_1=\frac{15 - 22}{2.5}=\frac{- 7}{2.5}=-2.8$. For $x = 30$, $z_2=\frac{30 - 22}{2.5}=\frac{8}{2.5}=3.2$.

Step2: Use z - table

The area to the left of $z_1=-2.8$ from the z - table is $0.0026$. The area to the right of $z_2 = 3.2$ is $1 - 0.9993=0.0007$.

Step3: Find total proportion

The proportion of rejected tomatoes is $0.0026+0.0007 = 0.0033$.