1. For a standard normal random variable Z, find (a) P(0 ? Z ? 1.56) (b) P(Z ? 2
ID: 3223275 • Letter: 1
Question
1. For a standard normal random variable Z, find
(a) P(0 ? Z ? 1.56)
(b) P(Z ? 2.00)
(c) P(|Z| < 1.78)
(d) P(?1.45 < Z < 2.65)
(e) Z0 such that P(Z < Z0) = 0.9750
(f) Z0 such that P(Z > Z0) = 0.0054
3. For the previous problem, find the value of X which represents the 95th percentile.
4. The probability that a patient recovers from a rare blood disease is 0.4. If 100 people are known to have contracted the disease, what is the probability that less than 30 survive? (Use a normal approximation of a binomial distribution. Be sure to include a correction for continuity.)
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As per forum rules attempting Q1 :
a.P(0<=Z<=1.56) = .9406-.5 = .4406
b.P(Z<=2) = .95
c.P(|Z|<1.78) = 2*(.9625-.5) = .925
d.P(-1.45<Z<2.65) = .9960-.0735 = .9225
e.P(Z<Z0) = .9750, Z0 = 1.96
f.P(Z>Z0) = .0054, Z0 = 2.54
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