Question

Assume that the scores on the bench press are normally distributed. Who has to improve the least to reach their goal (with regards to additional pounds they will have to lift)?

a. Someone who is at 10th percentile who wants to reach the 15th percentile

b. someone who is at 45th percentile who wants to reach the 50th percentile

c. someone who is at 65th percentile who wants to reach the 70th percentile

d. someone who is at 75th percentile who wants to reach 80th percentile.

Explain WHY

Answer 1

b. someone who is at 45th percentile who wants to reach the 50th percentile

The normal distribution curve in bell or mound shaped, in which the slope is highest near the mean and it flattens as we go away from the mean. So, a little change in variable X will cause a larger change in probability value if X is near the mean and as we go farther from the mean, the change in X value will have lesser and lesser impact on probability. The reason for this is that, most number of people have scores which are closer to the mean and hence, a little improvement near means you are overtaking larger number of people, when compared to points farther from mean. 50 percentile is the mean and 45th to 50 percentile is the closes interval to mean given in the option. So, someone who is at 45th percentile who wants to reach the 50th percentile has to improve the least to reach their goal.