a What is the probability that an iPad Mini of the same spec

(a.) What is the probability that an iPad Mini of the same specs, chosen randomly from a dealer, will cost less than $460? (Show your work).

(b.) What is the probability that an iPad Mini of the same specs, chosen randomly from a dealer, will cost greater than $549? (Show your work).

(c.) What is the probability that an iPad Mini of the same specs, chosen randomly from a dealer, will cost between $525 and $545? (Show your work).

(d.) The manufacturer doesnt want dealers to markup these iPad Minis above the 90th percentile of the price distribution. Approximately, what is the 90th percentile of the distribution of the price of this iPad Mini? Show your work. (e.) What is the probability that the average price of 25 iPad Minis of the same specs, chosen randomly from a dealer, will be greater than $510? (Show your work).

(f.) Compute the probability that at least 4 out of 5 iPad Minis of the same specs picked randomly from among dealers will cost between $525 and $545?

The price of a particular make of a 64GB iPad Mini among dealers nationwide is assumed to have a Normal distribution with mean = $500 with standard deviation sigma = $20. (a.) What is the probability that an iPad Mini of the same specs, chosen randomly from a dealer, will cost less than $460? (Show your work). (b.) What is the probability that an iPad Mini of the same specs, chosen randomly from a dealer, will cost greater than $549? (Show your work). (c.) What is the probability that an iPad Mini of the same specs, chosen randomly from a dealer, will cost between $525 and $545? (Show your work). (d.) The manufacturer doesn\'t want dealers to markup these iPad Minis above the 90th percentile of the price distribution. Approximately, what is the 90th percentile of the distribution of the price of this iPad Mini? Show your work. (e.) What is the probability that the average price of 25 iPad Minis of the same specs, chosen randomly from a dealer, will be greater than $510? (Show your work). (f.) Compute the probability that at least 4 out of 5 iPad Minis of the same specs picked randomly from among dealers will cost between $525 and $545?

Solution

(a.) What is the probability that an iPad Mini of the same specs, chosen randomly from a dealer, will cost less than $460? (Show your work).

P(X<460) = P((X-mean)/s <(460-500)/20)

=P(Z<-2) = 0.0228 (from standard normal table)

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(b.) What is the probability that an iPad Mini of the same specs, chosen randomly from a dealer, will cost greater than $549? (Show your work).

P(X>549) = P(Z>(549-500)/20)

=P(Z>2.45) = 0.0071 (from standard normal table)

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(c.) What is the probability that an iPad Mini of the same specs, chosen randomly from a dealer, will cost between $525 and $545? (Show your work).

P(525<X<545) = P((525-500)/20<Z<(545-500)/20)

=P(1.25<Z<2.25) = 0.0934 (from standard normal table)

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(d.) The manufacturer doesn