Respuesta :
Answer:
0.0228
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
This means that [tex]\mu = 200, \sigma = 25[/tex]
The probability of a player weighing more than 250 pounds is
This is 1 subtracted by the pvalue of Z when X = 250. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{250 - 200}{25}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
The probability of a player weighing more than 250 pounds is 0.0228
