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The weight of tomatoes chosen at random from a bin at the farmer's market follows a Normal distribution with mean μ=10ounces and standard deviation σ=1ounce. 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.

Short Answer

Expert verified

(b) T is a random variable with a mean of 40 ounces and a standard deviation of 2 ounces.

Step by step solution

01

Given Information

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,

t~N10,12
02

Explanation for correct option

According to the information provided,

t~N10,12

As a result of the normal distribution property,

nt~Nn(10),nI2

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

T≈4t~N4(10),412T~N40,22

Thus, the correct option is "b".

03

Explanation for incorrect option

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.

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