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Question #3
Suppose the average score on a national exam is
500 with a standard deviation of 100 . If each score is increased by 20 and the result is increased by 10 percent, what are the new mean and standard deviation?
(A)
mu=570,sigma=100
(B)
mu=570,sigma=110
(C)
mu=572,sigma=100
(D)
mu=572,sigma=110
(E)
mu=572,sigma=132

Question \# $3$ $\newline$ Suppose the average score on a national exam is $\mathbf{5 0 0}$ with a standard deviation of $100$ . If each score is increased by $20$ and the result is increased by $10$ percent, what are the new mean and standard deviation? $\newline$ (A) $\mu=570, \sigma=100$ $\newline$ (B) $\mu=570, \sigma=110$ $\newline$ (C) $\mu=572, \sigma=100$ $\newline$ (D) $\mu=572, \sigma=110$ $\newline$ (E) $\mu=572, \sigma=132$

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Find values of normal variables

Full solution

Q. Question \#

3

\newline

Suppose the average score on a national exam is

\mathbf{5 0 0}

with a standard deviation of

100

. If each score is increased by

20

and the result is increased by

10

percent, what are the new mean and standard deviation?

\newline

(A)

\mu=570, \sigma=100

\newline

(B)

\mu=570, \sigma=110

\newline

(C)

\mu=572, \sigma=100

\newline

(D)

\mu=572, \sigma=110

\newline

(E)

\mu=572, \sigma=132

Calculate New Mean: Calculate the new mean after adding $20$ to each score. $\newline$ Original mean ( $\mu$ ) = $500$ $\newline$ New mean after adding $20$ = $500 + 20 = 520$
Calculate Mean After $10$ % Increase: Calculate the new mean after increasing by $10$ percent. $\newline$ New mean after $10$ % increase = $520 \times 1.10 = 572$
Calculate New Standard Deviation: Calculate the new standard deviation after adding $20$ to each score. $\newline$ Original standard deviation ( $\sigma$ ) = $100$ $\newline$ Adding a constant to each score does not change the standard deviation, so $\sigma$ remains $100$ .
Calculate Standard Deviation After $10$ % Increase: Calculate the new standard deviation after increasing by $10$ percent. New standard deviation = $100 \times 1.10 = 110$

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