A construction company has an expenditure rate of E(x)equalse Superscript 0.11 x dollars per day on a particular paving job and
an income rate of I(x)equals116.8 minus e Superscript 0.11 x dollars per day on the same job, where x is the number of days from the start of the job. The company's profit on that job will equal total income less total expenditures. Profit will be maximized if the job ends at the optimum time, which is the point where the two curves meet. (a) Find the optimum number of days for the job to last. (b) Find the total income for the optimum number of days. (c) Find the total expenditures for the optimum number of days. (d) Find the maximum profit for the job.
1 answer:
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Using the normal distribution, it is found that 25.14% of the batteries will last more than 420 hours.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, we have that the mean and the standard deviation are given, respectively, by:
.
The proportion of the batteries will last more than 420 hours is <u>one subtracted by the p-value of Z when X = 420</u>, hence:
Z = 0.67
Z = 0.67 has a p-value of 0.7486.
1 - 0.7486 = 0.2514.
0.2514 = 25.14% of the batteries will last more than 420 hours.
More can be learned about the normal distribution at brainly.com/question/24663213
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