Question

"Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric.
In 1993, actress Anna Paquin won an academy award in for the movie ""The Piano."" She was 11-years-old. Finish the statement: ""According to the Empirical Rule, the ages of nearly all lead actresses will be between______________and_____________ years. Anna Paquin was this range when she won the academy award."""

a) 10.6; 48.7; within
b) 23.3: 36.0; within
c) 16.9: 42.3; not within
d) 10.6: 48.7; not within

Answer 1

Answer:

a) 10.6; 48.7; within

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 29.6

Standard deviation = 6.35

"According to the Empirical Rule, the ages of nearly all lead actresses will be between______________and_____________ years.

Nearly all(99.7%) will be within 3 standard deviations from the mean.

So from 29.6 - 3*6.35 = 10.6 years to 29.6 + 3*6.35 = 48.7 years.

Anna was 11-years old, so she was within this range.

So the correct answer is

a) 10.6; 48.7; within