PROBLEM 5 X is a normal random variable with = 20, = 4. For each of (a)-(c), fin

Question

PROBLEM 5

X is a normal random variable with = 20, = 4. For each of (a)-(c), find x so that: (a) P(X x) = 0.33, (b) P(X x) = 0.47, (c) P(x < X x) = 0.69.

PROBLEM 6

Suppose you flip a coin three times; the coin is bent in such a way that the probability of H is 1/3. What is the probability that you get at least one H? Solve the problem in two ways: by using the binomial distribution (easy) and by using what we learned in Lecture 2 (less easy).

PROBLEM 7

Assume you are purchasing a large quantity of markers for the University and that your supplier guarantees that the shipment will contain no more than 2% defectives. To test, you randomly select 10 markers (with replacement) and you find one defective. Based on this evidence, do you think the supplier has complied with the guarantee?

Explanation / Answer

X is a normal random variable with = 20, = 4.

For each of (a)-(c), find x so that:

(a) P(X x) = 0.33,

P(Z<z*) =0.33

z* = -0.439

X = + z

= 20 -0.439*4 = 18.244

(b) P(X x) = 0.47,

P(Z>z*) = 0.47

z* = 0.075

X = + z

= 20 +0.075*4 = 20.3

(c) P(x < X x) = 0.69.

P(X< x) = 0.5+0.69/2 =

P(Z<z*) = 0.845

z* =1.015

X = 20 +1.015*4 =24.06

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