Respuesta :
Answer:
0.8413 = 84.13% probability that a bolt has a length greater than 2.96 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.
Mean of 3 cm and a standard deviation of 0.04 cm.
This means that [tex]\mu = 3, \sigma = 0.04[/tex]
What is the probability that a bolt has a length greater than 2.96 cm?
This is 1 subtracted by the p-value of Z when X = 2.96. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.96 - 3}{0.04}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
1 - 0.1587 = 0.8413
0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.
