Math 117 Practice Midterm 2

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

Printable Key

Problem 1

The following table gives the probability distribution for the number of kittens in a litter.

 Number x in Litter 1 2 3 4 5 6 P(x) 0.05 0.12 0.24 0.35 0.2 0.04

Determine E(x) and s.  Explain the meaning of each.

Solution

Problem 2

You have experimented with the days for germination for a lupin and know that the distribution follows the parabolic distribution

f(t)  =  kt(1 - t)        for         0  <  t  < 1

where t is measured in months and k is a positive constant.

A.  Find k.

Solution

B.  Find the probability that a lupine seed will germinate between 0.3 and 0.5 months.

Solution

C.  Find the expected value E(t) and interpret what it means.

Solution

D.  Find the standard deviation.

Solution

Problem 3

Currently, the benefit package costs the college \$9442 and is expected to increase 20% next year.  Assume the 20% increase becomes a trend over the next several years.

A.  Write an expression for the cost of the benefit package after n years.

Solution

B.  Compute the cost of benefits in the year 2020.  (This year is 2004).

Solution

Problem 4

Determine the convergence or divergence of the following series.

A.

Solution

B.

Solution

C.

Problem 5

Explain why the series converges.  Then approximate the following sum using 5 terms.  Then estimate the maximum error of your approximation.

Solution