Answer:
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 and standard deviation
, the zscore of a measure X is given by:
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:
He decides to sell boats that will appeal to the middle 66% of the market in terms of price.
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.
83rd percentile
X when Z has a pvalue of 0.83. So X when Z = 0.955.
The maximum price that the dealer will sell is $7471 and the minimum is $5513.