At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the number of loans X that a randomly selected loan agent closes on a randomly selected day has the probability distribution below. x 1 2 3 4 5 6 7p(x) 0.05 0.10 0.22 0.30 0.18 0.12 0.03 At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let YY represent the amount of money made by a randomly selected loan agent on a randomly selected day. Which of the following statements is NOT true?A. The mean of X is less than the mean of Y. B. The standard deviation of Y is approximately $71. C. The mean daily salary is greater than $350 per day. D. The standard deviation of X is less than the standard deviation of Y. E. The shape of the probability distribution of Y is unimodal and roughly symmetric.

The mean daily salary is greater than $350 per day and this can be determined by using the given data.

Given :

At a certain company, loan agents are paid based on the number of loans they close in a day.

The computation is given by:

Y = a + bX

where Y is the money made by randomly selected, a is $150, b is $50, and X is the number of loans.

Now, the value of E(x) is given by:

Now, the value of E(y) is given by:

E(y) = $347

So, the correct option is given by C) The mean daily salary is greater than $350 per day.

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C. The mean daily salary is greater than $350 per day

Step-by-step explanation:

The computation is shown below:

Y = a + bX

where,

Y = money made by a random selected

a = $150

b = $50

X = number of loan

Now

E(x) = (1 × 0.05) + (2 × 0.10) + (3 × 0.22) + (4 × 0.30) + (5 × 0.18) + (6 × 0.12) + (7 × 0.03)

= 3.94

Now

E(y) = $150 + ($50 × 3.94)

= $347

hence, the option C is not correct