Asked by Justin Paquet on May 24, 2024
Verified
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.The probability of a player weighing less than 240 pounds is
A) 0.0548.
B) 0.9452.
C) 0.9956.
D) 0.0044.
Standard Deviation
A measure of the amount of variation or dispersion of a set of values, indicating how much the individual data points differ from the mean of the data.
Normally Distributed
Describes a symmetrical bell-shaped distribution of data points, where most of the data points cluster around a central peak and the probabilities for values farther from the mean taper off symmetrically in both directions.
Football Players
Individuals who participate in the sport of football, which involves competing to score goals against an opposing team.
- Cultivate an understanding of the attributes and practical uses of the normal distribution.
- Quantify the probabilities and percentages involved in normal distributions.
Verified Answer
JN
Jorge Nunez-IzaguirreMay 28, 2024
Final Answer :
B
Explanation :
We need to find the area under the normal distribution curve to the left of 240 pounds. Using a standard normal distribution table, we find the corresponding z-score to be 1.6. Therefore, the probability of a player weighing less than 240 pounds is the same as the probability of a standard normal variable being less than 1.6, which is 0.9452.
Learning Objectives
- Cultivate an understanding of the attributes and practical uses of the normal distribution.
- Quantify the probabilities and percentages involved in normal distributions.