The weight of tomatoes chosen at random from a bin at the farmer's market follows a Normal distribution with mean $\mu =10$ounces and standard deviation $\sigma =1$ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is

a. Normal, with mean 10 ounces and standard deviation 1 ounce.

b. Normal, with mean 40 ounces and standard deviation 2 ounces.

c. Normal, with mean 40 ounces and standard deviation 4 ounces.

d. binomial, with mean 40 ounces and standard deviation 2 ounces.

e. binomial, with mean 40 ounces and standard deviation 4 ounces.

The weight of tomatoes randomly selected from a bin at the farmer's market follows a normal distribution with a mean of ten and a standard deviation of one dollar.

Consider the random variable t, which is specified as the weight of tomatoes.

Therefore,

According to the information provided,

$t~N\left(10,1^2\right)$

As a result of the normal distribution property,

$nt~N\left(n\left(10\right),n\left({\mathrm{I}}^2\right)\right)$

As a result, the T random variable (4 tomatoes weight) will be used.

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

Thus, the correct option is "b".

Option (a) Normal, with mean 10 ounces and standard deviation 1 ounce is not the correct answer.

Option (c) Normal, with mean 40 ounces and standard deviation 4 ouncesis not the correct answer.

Option (d) binomial, with mean 40 ounces and standard deviation 2 ounces is not the correct answer.

Option (e) binomial, with mean 40 ounces and standard deviation 4 ounces is not the correct answer.