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?
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%.