Mathematics, 21.04.2020 16:21 faithtunison

A marine sales dealer Önds that the average price of a previously owned boat is $6492. He decides to sell boats that will appeal to the middle 66% of the market in terms of price. Find the maximum and minimum prices of the boats the dealer will sell. The standard deviation is $1025, and the variable is normally distributed.

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Answer from: rachelkim999

The maximum price that the dealer will sell is $7471 and the minimum is $5513.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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:

$\mu = 6492, \sigma = 1025$

Middle 66%

50 - (66/2) = 17th percentile

50 + (66/2) = 83rd percentile

17th percentile

X when Z has a pvalue of 0.17. So X when Z = -0.955.

$Z = \frac{X - \mu}{\sigma}$

$-0.955 = \frac{X - 6492}{1025}$

X - 6492 = -0.955*1025

X = 5513

83rd percentile

X when Z has a pvalue of 0.83. So X when Z = 0.955.

$Z = \frac{X - \mu}{\sigma}$

$0.955 = \frac{X - 6492}{1025}$

X - 6492 = 0.955*1025

X = 7471

The maximum price that the dealer will sell is $7471 and the minimum is $5513.

Answer from: Quest

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number $c\in[0.5,0.75]$ that satisfies the conclusion of the mean value theorem, that is, a number $c\in[0.5,0.75]$ such that

$f'(c) = \dfrac{f(0.75) - f(0.5)}{0.75-0.5},$

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

Answer from: Quest

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A marine sales dealer Önds that the average price of a previously owned boat is $6492. He decides to...

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