The average weight an NFL player is 245.7 pounds with standard deviation of 34.5 pounds but probability distribution of the popu
lation is unknown. If a random sample of 32 NFL players is selected, what is the probability that: (i) the average weight of the sample will be less than 234 pounds?
(ii) the average weight of the sample is between 248-254?
(iii) the average weight of the sample is between 242-251?
Answer: For part I, the probability is 36.69% that the average weight will be less than 234.
To find the percents for each one, you need to find the z-score and use a normal distribution table. A z-score is the number of standard deviations above or below the mean.
For 234, the z-score would be: (234 - 245.7) / 34.5 = -0.34 which corresponds to a percent of 36.69%.
For that last 2 parts, you follow the same plan. However, you will find two different percents. You will have to subtract them to find the percent between them.