Statistics and Probability Answers

An article in Fortune (September 21, 1992) claimed that nearly one-half of all engineers continue academic studies beyond the B.S. degree, ultimately receiving either an M.S. or a Ph.D. degree. Data from an article in Engineering Horizons (Spring 1990) indicate that 117 of 484 new engineering graduates were planning graduate study.

(a) Test the hypothesis; H0: p=0.5 versus H1: p is not equal 0.5. Use a=0.05


(b) What is the P-value for this test? Round your answer to 4 decimal places.

Let the sample size of the television tube brightness experiment be ten and the sample mean and sample standard deviation be 317.2 microamps and 15.7 microamps, respectively. Suppose that the design engineer claims that this tube will require at least 300 microamps of current to produce the desired brightness level.

Choose an appropriate hypothesis to test.

Find the P-value for this test.

0.25 < P-value < 0.50
0.025 < P-value < 0.050
0.0025 < P-value < 0.0050
0.0005 < P-value < 0.0010

The 2004 presidential election exit polls from the critical state of Ohio provided the following results. There were 2020 respondents in the exit polls and 768 were college graduates. Of the college graduates, 412 voted for George Bush.

(a) Calculate a 90% confidence interval for the proportion of college graduates in Ohio that voted for George Bush. Round the answers to 3 decimal places.

(b) Calculate a 95% lower confidence bound for the proportion of college graduates in Ohio that voted for George Bush. Round the answer to 3 decimal places.

The number of steps to cover the same distance was measured for 121 randomly chosen people. The sample mean is 3210 steps and the sample standard deviation is 642 steps.Assume the distribution to be normal. Round your answers to nearest integer.

Dairy cows at large commercial farms often receive injections of bST, a hormone used to spur milk production. Bauman et al. reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standard deviation of milk production is 2.25 kg/d.

A. Find the 99% confidence interval for the true mean milk production. (Round the answer to two decimal places)

B. If the farms want the confidence interval to be no wider than + - 1.10 kg/d, what level of confidence would they need to use? ( Round answers to the nearest integer) (Express the answer in percent)

1. A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. How is the standard of the sample mean changed when the sample size is increased from n=10 to n=47 ? Round all the intermediate calculations to four decimal places.

2. Suppose X has discrete uniform distribution

f(x) = { 1/3, x=1,2,3
{ 0, otherwise

A random sample of n=35 is selected from this population. Find the probability that the sample mean is greater than 2.1 but less than 2.4. Express the final answer to four decimal places.

A laptop company claims up to 8.1 hours of wireless web usage for its newest laptop battery life. However, reviews on this laptop shows many complaints about low battery life. A survey on battery life reported by customers shows that it follows a normal distribution with mean 7.5 hours and standard deviation 36 minutes.

(a) What is the probability that the battery life is at least 8.1 hours?
Round your answer to four decimal places (e.g. 98.7654).

(b) What is the probability that the battery life is less than 6.9 hours?
Round your answer to four decimal places (e.g. 98.7654).

(c) What is the time of use that is exceeded with probability 0.9?
Round your answer to two decimal places (e.g. 98.76).

Integration by parts is required. The probability density function for the diameter of a drilled hole in millimeters is

10e^(-10(x-60)) for x > 6.0 mm


Although the target diameter is 6.0 millimeters, vibrations, tool wear, and other nuisances produce diameters larger than 6.0 millimeters.



a) Determine the mean and variance of the diameter of the holes.

Mean = _______ (Round your answer to 1 decimal place.)
Variance = ______ (Round your answer to 2 decimal places.)

b) Determine the probability that a diameter exceeds 6.1 millimeters. (Round your answer to 3 decimal places.)

The talk time (in hours) on a cell phone in a month is approximated by the probability density function.

f(x) = x-5 / 5h for 5 < x < 10, 1/h for 10 less than or equal to x less than or equal to 15, - x-20 / 5h for 15 less than or equal to x less than or equal 20.

Determine the following:

a. h
b. P(X<30) Round the answers to two decimal places.
c. P(X<16.0) Round the answers to two decimal places.
d. x such that P(X<x)=0.95

1. Circle the right Answer.
There were total 1020 members in BMCC Math Club. 50% of them are female. 45 out of 1020 are from Prof. X’s class. 20% of 45 students are international students. In order to join in the Math Club, students must take one exam. You can take the exam as many times as you want. Members meet every Wednesday in Room N736. (10 points)
a. 50% is a. Parameter or Statistic
b. 20% is a. Parameter or Statistic
c. 1020 is. Quantitative or Categorical
d. 736 is. Quantitative or Categorical
e. The number of times Continous or Discrete

2. At a recent chess tournament, all 15 of the participants had to fill out a form that gave their names, address and age. The ages of the participants were recorded as follows: 36, 48, 54, 92, 57, 63, 66, 76, 66, 80, 82, 65, 39, 77, and 45. Use the data to construct a frequency table and histogram with 3 classes.(15 points)
Classes. Class Boundaries. Frequency. Midpoint. Cumulative Frequency