Respuesta :
Answer:
0.3557 = 35.57% probability that one selected subcomponent is longer than 118 cm.
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.
Normally distributed with a mean of 116 cm and a standard deviation of 5.4 cm.
This means that [tex]\mu = 116, \sigma = 5.4[/tex]
Find the probability that one selected subcomponent is longer than 118 cm.
This is 1 subtracted by the pvalue of Z when X = 118. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{118 - 116}{5.4}[/tex]
[tex]Z = 0.37[/tex]
[tex]Z = 0.37[/tex] has a pvalue of 0.6443
1 - 0.6443 = 0.3557
0.3557 = 35.57% probability that one selected subcomponent is longer than 118 cm.
