The average price of personal computers manufactured by the MNM company is $1,20

Question

The average price of personal computers manufactured by the MNM company is $1,200 with a standard deviation of $220. It is known that the computer prices are normally distributed. Complete the following question using Excel.

In blank #1 enter the probability that a computer has a price of at most $978. (Round your answer to 4 decimal places and enter your answer as 0.1234 and not .1234.)

In blank #2 enter the probability that a computer has a price between $1000 and $1400. (Round your answer to 4 decimal places and enter your answer as 0.1234 and not .1234.)

20% of the computers have a price less than what number? Enter your answer in blank #3. (Round your answer to 2 decimal places and enter your answer as $1234.67, including the $ sign.)

Computers with prices of more than $1600 receive a discount. Enter the percentage of computers that receive a discount in blank #4. (Round your answer to 2 decimal places and enter your answer as 1.23%, including the percent sign.)

Explanation / Answer

1) probability that a computer has a price of at most $978=P(X<978)=P(Z<(978-1200)/220)=P(Z<-1.0091)=0.1565

(=normsdist(-1.0091))

2) probability that a computer has a price between $1000 and $1400 =P(1000<X<1400)=P(-0.9091<Z<0.9091)

=0.8183-0.1817 =0.6367 (=normsdist(0.9091)-normsdist(-0.9091))

3)for 20th percentile ; z=-0.8416 (normsinv(0.20))

therefore corresponding price =mean +z*std devition =$1014.84

4)here percentage of computers that receive a discount in blank=P(X>1600)=1-P(X<1600)=1-P(Z<1.8182)

=1-0.9655 =0.0345 ~~ 3.45%

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