Review for Test 2 MAT 200
1) Compute the mean, variance, and standard deviation of the following probability distribution.
X / 2 / 4 / 6 / 8P(x) / 0.15 / 0.30 / 0.25 / 0.30
2) An emergency life-support system has six batteries. The probability of any battery not failing is .95. What is the probability that
a) none fail? b) all fail? c) at least 2 fail? d) exactly 4 fail? e) between 3 and 5 fail?
f) Why is this problem a binomial distribution? What are n and p?
3) Louis N. Clark discovers that the distribution of heights of students in his class is normally distributed with a mean of 140 cm and a standard deviation of 10 cm. Answer the following questions about the distribution of heights for Louis’ class:
a) What percent of heights are below 148?
b) What percent of heights lie between 133 and 144?
c) What percent of heights lie above 138?
d) What percent of heights are within 1 standard deviation of the mean?
e) Find the height of a student that would be at the 75th percentile.
4) Find the area under the standard normal curve for each of the following regions:
a) to the right of z = - 2.56 b) between the values of z = -0.34 and z = 2.45.
5) A pair of loaded dice has P(rolling sum of 7) = .65. The dice are rolled 400 times. Answer the following:
a) P(rolling more than 253 sevens) =
b) P(rolling at most 257 sevens) =
c) P( rolling between 258 and 262 sevens, inclusive) =
d) Using these loaded dice, Jim Nasium rolls a certain number of sevens. The probability of rolling at most as many sevens as Jim did is .68. How many sevens did Jim Nasium roll?