Respuesta :
Answer:
27.02% of boys aged 16 to 17 will not be able find shoes that fit in this store
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions 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.
Mean of 25.5 centimeters and a standard deviation of 1.4 centimeters.
This means that [tex]\mu = 25.5, \sigma = 1.4[/tex]
These shoes will fit men with feet that are 24.6 to 28.8 centimeters long. What percentage of boys aged 16 to 17 will not be able find shoes that fit in this store?
Less than 24.6:
The proportion is the pvalue of Z when X = 24.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24.6 - 25.5}{1.4}[/tex]
[tex]Z = -0.64[/tex]
[tex]Z = -0.64[/tex] has a pvalue of 0.2611
More than 28.8:
The proportion is 1 subtracted by the pvalue of Z when X = 28.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28.8 - 25.5}{1.4}[/tex]
[tex]Z = 2.36[/tex]
[tex]Z = 2.36[/tex] has a pvalue of 0.9909
1 - 0.9909 = 0.0091
0.2611 + 0.0091 = 0.2702
0.2702*100% = 27.02%
27.02% of boys aged 16 to 17 will not be able find shoes that fit in this store
