Question

The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at an awards ceremony. The distributions of the ages are approximately​ bell-shaped. Compare the​ z-scores for the actors in the following situation.

Best Actor		Best Supporting Actor
μ equals=44.0		μ equals=49.0
sigma σ equals=6.7		sigma σ equals=14

In a particular​ year, the Best Actor was 37 years old and the Best Supporting Actor was 53 years old.

Determine the​ z-scores for each.

Best Actor		z	equals=
Best Supporting Actor:		z	equals=

The Best Actor was ____ to the​ mean, and the Best Supporting Actor was ___ to the mean.

choices for the blanks-

less than two standard deviations below

more than 1 standard deviation above

about one standard deviation below

more than 2 standard deviations above

question- One, Both, or Neither of their ages​ is/are unusual???

Answer 1

z-score =

z-score explains how much 'x' a value is away from its mean in terms of SD, if it is less than mean then z-score will be negative and vice versa

	Best Actor	Best Supporting Actor
μ	44	49
σ	6.7	14
z-score	(x - 44)/6.7	(x-49)/14
x	37	53
z-score	-1.04	0.29
Comment	less than mean by more than 1SD	more than mean but less than 1SD

The Best Actor was __about one standard deviation below__ to the​ mean, and the Best Supporting Actor was _more than 1 standard deviation above__ to the mean.

less than two standard deviations below

more than 1 standard deviation above

about one standard deviation below

more than 2 standard deviations above

it is actually less than 1 SD above mean for the supporting actor but the closest option has been chosen.

Events which falls outside the range of z-scores of (-1.96 < z < 1.96) are generally unusual. But since both the z-scores fall within this range it is not unusual.

question- One, Both, or Neither of their ages​ is/are unusual???

Neither of their ages​ are unusual