Respuesta :
Answer:
340
Step-by-step explanation:
The first step is finding the percentage of those who fail within 19 months.
Problems of normally distributed samples 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.
In this problem, we have that:
[tex]\mu = 18.2, \sigma = 1.7[/tex]
The proportion is the pvalue of Z when X = 19. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 18.2}{1.7}[/tex]
[tex]Z = 0.47[/tex]
[tex]Z = 0.47[/tex] has a pvalue of 0.6808.
Jolt is expected to replace 0.6808 of the connectors sold. Out of 500, that is, on average, 0.6808*500 = 340.
Jolt expects to replace, on average, 340 of the connectors sold.
