Chapter 6, Problem T6.6SPT

To determine

To find:The distribution of random variable T.

Answer to Problem T6.6SPT

The random variable T follows normal with mean 40 ounces and standard deviation 2 ounces.

Explanation of Solution

Given:

The weight of tomatoes chosen at random from a bin at the farmer’s market follows a Normal distribution with mean 10 and standard deviation 1.

Consider that t is defined as the random variable defined as the weight of tomatoes.

Therefore,

  $t\sim N\left(10,1^2\right)$

Calculation:

As per the given information,

  $t\sim N\left(10,1^2\right)$

From the property of normal distribution,

  $nt\sim N\left(n\left(10\right),n\left(1^2\right)\right)$

Therefore, T random variable (4 tomatoes weight) will follow,

  $\begin{array}{l}T\approx 4t\sim N\left(4\left(10\right),4\left(1^2\right)\right)\\ T\sim N\left(40,2^2\right)\end{array}$

Thus, the correct option is “b”.