Respuesta :
Answer:
c. .0069
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 22 and a standard deviation of 5.
This means that [tex]\mu = 22, \sigma = 5[/tex]
The probability that x is less than 9.7 is
This is the p-value of Z when X = 9.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.7 - 22}{5}[/tex]
[tex]Z = -2.46[/tex]
[tex]Z = -2.46[/tex] has a p-value of 0.0069, and thus, the correct answer is given by option c.
