Given a normal distribution with mu= 35 and sigma =6,

find (a) the normal curve area to the right of x=18;

(b) the normal curve area to the left of x =28;

(c) the normal curve area between x= 42 and x= 46;

(d) the value of x that has 80% of the normal curve area to the left; and (e) the two values of x that contain the middle 75% of the normal curve area.

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2) A pair of dice is rolled 180times. What is the probability that a total of 7 occurs

(a) at least 22 times?

(b) between 34 and 42 times inclusive?

(c) exactly 30 times?

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3) A common practice of airline companies is to sell more tickets for a particular flight than there are seats on the plane, because customers who buy tickets do not always show up for the flight. Suppose that the percentage of no-shows at flight time is 3%. For a particular flight with 173 seats, a total of 175 tickets were sold. What is the probability that the airline overbooked this flight?

4)

The life, in years, of a certain type of electrical switch has an exponential distribution with an average life beta=4. If 400 of these switches are installed in different systems, what is the probability that at most 75 fail during the first year?