Respuesta :
Answer:
0.3413 = 34.13% probability that the crew member earns between $20.50 and $24.00 per hour
Step-by-step explanation:
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.
A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50.
This means that [tex]\mu = 20.5, \sigma = 3.5[/tex]
a. Between $20.50 and $24.00 per hour
This is the pvalue of Z when X = 24 subtracted by the pvalue of Z when X = 20.5. So
X = 24
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 20.5}{3.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
X = 20.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20.5 - 20.5}{3.5}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
0.8413 - 0.5 = 0.3413
0.3413 = 34.13% probability that the crew member earns between $20.50 and $24.00 per hour
