Question

When Jack goes bowling, his scores are normally distributed with a mean of115 and a standard deviation of 11. What is the probability that the next gameJack bowls, his score will be higher than 95, to the nearest thousandth?

Answer 1

We know that

• The mean is 115.

,

• The standard deviation is 11.

,

• The given value is x = 95.

Let's use the Empirical Rule to find the answer:

• 68% of the measures are with 1 standard deviation of the mean.

,

• 95% of the measures are with 2 standard deviations of the mean.

,

• 99.7% of the measures are with 3 standard deviations of the mean.

So, we just have to use the mean, the standard deviation, and the given value to find the correct percentage that represents the probability. The image below shows the distribution.

As you can observe, we subtracted the standard deviation from the mean to identify the interval where x = 95 is in.

Hence, the probability of a score higher than 95 is 0.975