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. what proportion of such tomatoes have a diameter between 20 and 26 mm? find the z - table here. 0.2667 0.4237 0.5763 0.7333

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. what proportion of such tomatoes have a diameter between 20 and 26 mm? find the z - table here. 0.2667 0.4237 0.5763 0.7333

Answer

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 22$ (mean), $\sigma=2.5$ (standard deviation). For $x = 20$, $z_1=\frac{20 - 22}{2.5}=\frac{-2}{2.5}=- 0.8$. For $x = 26$, $z_2=\frac{26 - 22}{2.5}=\frac{4}{2.5}=1.6$.

Step2: Use the z - table

From the z - table, the area to the left of $z_1=-0.8$ is $0.2119$. The area to the left of $z_2 = 1.6$ is $0.9452$.

Step3: Find the proportion

The proportion of tomatoes with diameter between 20 and 26 mm is $P(-0.8<Z<1.6)=P(Z < 1.6)-P(Z < - 0.8)=0.9452-0.2119 = 0.7333$.

Answer:

0.7333