Question: 1)Let X be a normal random variable with meanand standard deviation . Find Pr [- < X < + ] 2)Xis a normal random variable

1)Let X be a normal random variable with meanand standard deviation. Find Pr [- < X < +]

2)Xis a normal random variable with standard deviation=5. If Pr[X< 30] = .8413, what is the mean ofX.

3)Smerteescandies are packaged in boxes. The number ofSmerteesin each box is approximately normally distributed, with mean 32 and standard deviation 4. What is the probability that when you buy a box ofSmerteesyou will get fewer than 35 candies?

4)A fair die is tossed 180 times. What is the probability that a 2 comes up no more than 32 times in these 180 tosses?

5)Which of the following expressions is a suitable approximation (using the normal distribution) for the probability thatat most35 "sixes" are obtained in 180 tosses of a fair die?

A. Pr[Z < 4.5/5]

B. Pr[Z < or equal to 5.5/5]

C. Pr [Z < 25/4.5]

D. Pr [Z < 180-35.5/5]

E. Pr [Z < or equal to 34.5/25

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