I really dont understand please help 1 costs range from 4000

I really don\'t understand please help

1) costs range from $4,000 to $10,000 a year. Suppose costs are normally distributed with a mean equal to $7,000 and a standard deviation equal to $1,000.

a) what percentage will cost between $6,000 and $8,000

b) what percentage will cost between $5,000 and $9,000

c) what percentage will cost between $4,000 and $10,000

2) the expected price in 1998 for books was $400. Suppose the price of books is normally distributed with a standard deviation of $150. what percentage of the e-books being sold in 1998 were priced:

a) between $300 and $600

b) between $200 and $800

c) less than $250

d) over $900

3) in 2001 ACT students has a mean reading score of 21.3 with a standard deviation of 6.0. Assume that the scores are normally distributed

a) reading score lower than 20

b) reading score between 18 and 24

c) reading score higher than 30

d) find the value of the 75th percentuke for act scores

4) a coffee machine is adjusted to fill quart bottles mean= 32.0 oz of ale and a variance of 0.003. Periodically a bottle is checked and the amount of ale is notes.

a) assuming the amount of fill is normally distributed, what is the probabiluty that the next randomly checked bottle contains 32.02 oz

b) you buy 100 quart bottles of this ale for a party. how many bottles would you expect to maintain more than 32.02 oz?

Solution

1) P(6000<x<8000) = 68%

2) P(5000<x<9000) = 90%

3)  P(4000<x<10000) = 99.5%(Areas between mu-sigma, mu-2sigma and mu-3sigma on either side)

---------------------------------------------

2)P(300<x<600) = P(-0.67<z<1.33) = 65.68%

P(200<x<800) = P(-1.33<z<2.67) = 90.44%

P(X<250) =P(Z<1) = 0.1587

P(X>900) <0.0010

-------------------------------------

For 300 points more questions answered