Question

When Helen Mirren won the Oscar for Best Actress, she was 61 years old. The Oscar-winning Best Actresses had a mean age of 35.8 years and a standard deviation of 11.3 years. What is the difference between Helen Mirren's age and the mean age?

Answer 1

Answer:

a) $61-35.8=25.3$

b) $\frac{25.2}{11.3}=2.23$ deviations

c) $z = \frac{61- 35.8}{11.3}= 2.23$

d) For this case since we have that z>2 we can consider this value as unusual, since is outside of the interval considered usual.

Step-by-step explanation:

Assuming this complete question : "Helen Mirren was 61 when she earned her Oscar-winning Best Actress award. The Oscar-winning Best Actresses have a mean age of 35.8 years and a standard deviation of 11.3 years"

a) What is the difference between Helen Mirren’s age and the mean age?

For this case we can do this:

$61-35.8=25.2$

b) How many standard deviations is that?

We just need to take the difference and divide by the deviation and we got:

$\frac{25.2}{11.3}=2.23$ deviations

c) Convert Helen Mirren’s age to a z score.

The z score is defined as:

$z = \frac{x- \mu}{\sigma}$

And if we replace the values given we got:

$z = \frac{61- 35.8}{11.3}= 2.23$

d) If we consider “usual” ages to be those that convert to z scores between –2 and 2, is Helen Mirren’s age usual or unusual?

For this case since we have that z>2 we can consider this value as unusual, since is outside of the interval considered usual.