When Hudson goes bowling, his scores are normally distributed with a mean of 185 and a standard deviation of 14. What is the probability that the next game Hudson bowls, his score will be less than 160, to the nearest thousandth?

Answer 1

To find the probability that Hudson's score will be less than 160, we need to calculate the z-score for 160 and then find the corresponding area under the normal distribution curve.

The z-score is calculated using the formula:

z = (X - μ) / σ

where X is the score (160), μ is the mean (185), and σ is the standard deviation (14).

z = (160 - 185) / 14
z = -25 / 14
z ≈ -1.786

Now, we need to find the probability of the score being less than 160, which is the area to the left of z = -1.786 on the standard normal distribution table. Looking this z-score up in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.037.

Therefore, the probability that Hudson's score will be less than 160 in the next game is approximately 0.037 or 3.7%.