Answer:
15.87%, that is, approxiately 16% of of her shots will travel less than 23 feet.
Step-by-step explanation:
Problems of normally distributed samples can be solved using 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.
In this question, we have that:
[tex]\mu = 26, \sigma = 3[/tex]
Approximately what percentage of her shots will travel less than 23 feet?
This is the pvalue of Z when X = 23. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{23 - 26}{3}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587.
15.87%, that is, approxiately 16% of of her shots will travel less than 23 feet.
