1. Given a normal distribution with μ = 30 and σ = 6, determine the likelihood of the following events. ( Be certain to draw a graph! )
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:
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
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) = _____________________________
Where Sx = sample standard deviation of X
r = Cov(X,Y)/ (S_{x}S_{y}) = ________________ 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
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