Question

# 1.    Given a normal distribution with μ = 30 and σ = 6, determine the likelihood...

1.    Given a normal distribution with μ = 30 and σ = 6, determine the likelihood of the following events. ( Be certain to draw a graph! )

1. X < 36
1. X > 24?

c.     Between what two X values (symmetrically distributed around the mean) are 95%

of the values?

2.   A student is taking a multiple-choice test in which each question has five choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place five balls (marked A, B, C, D and E) into a box. She randomly selected one ball for each question and replaces the ball in the box. The marking on the will determine her answer to the question. There are 6 multiple-choice questions on the test. What is the probability that she will correctly answer the following:

1. five questions correct?
1. at most three questions correct?

3. The following is a set of data from a sample of n = 6 items:

X            8      6     9     5     7      10                       Xbar = arithmetic average of X

Y            21   16   24   17     18    30                      Ybar = arithmetic average of Y

1. Compute the covariance = Cov(X,Y)
 X Y X - Xbar Y – Ybar (X – Xbar)(Y – Ybar) (X – Xbar)2 (Y – Ybar)2

Cov(X,Y) = ∑( (X –Xbar)(Y – Ybar))/ ( n – 1)   =    _____________________________

1. Compute the coefficient of correlation

Where Sx = sample standard deviation of X

r =   Cov(X,Y)/ (SxSy) = ________________                 Sy = sample standard deviation of Y

c.    How strong is the relationship between X and Y?   Explain.

4.    A box contains 3 red balls and 5 green balls.

a. How likely is it that a red ball is drawn from the box?

b. How likely is it that green ball is drawn from the box?

c. How likely that if I draw a green ball and then a red ball from the box?

Assume without Replacement:

Assume with Replacement:

5. The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35%. Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work. Determine the probability that a visit to a PCP’s office results in both lab work and referral to a specialist.

Hint: Construct a Contingency Table

1. a. Here we need to find

As distribution is normal we can convert x to z

b. Here we need to find

c. Here we need to find x1 and x2 such that

Using z table we get

So

Hence

Similarly

So

So x1=18.24 and x2=41.76