QUESTION 21
The finishing process on new furniture leaves slight blemishes. The table below displays a manager's probability assessment of the number of blemishes on one piece of new furniture.
Number of Blemishes
0
1
2
3
4
5
Probability
0.34
0.25
0.19
0.11
0.07
0.04
1. On average, how many blemishes do we expect on one piece of new furniture?
2. What is the variance of blemishes on one piece of new furniture? (round to the nearest hundredth)
QUESTION 22
The probability that a person catches a cold during the cold-and-flu season is 0.4. Assume that 10 people are chosen at random.
On average, how many of these ten people would you expect to catch a cold?
What is the standard deviation of the number of
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Over the course of a month, a household receives 100 pieces of unsolicited mail.
What is the mean of the sample proportion of pieces of unread mail? (express as a decimal, not a percentage)
What is the standard error of the sample proportion?
What is the probability that the sample proportion is greater than 0.60? (express as a decimal, not a percentage)
ANSWERS
QUESTION 21 1. On average, how many blemishes do we expect on one piece of new furniture?
2. What is the variance of blemishes on one piece of new furniture? (round to the nearest hundredth)
QUESTION 22 p = 0.4 q = 1-p = 1-0.4 = 0.6 n = 10
1) Mean = np = 10*0.4 = 4
2) Standard deviation = sqrt [npq]
= sqrt [10*0.6*0.4]
= 1.5492
QUESTION 23
The number of nails in a five-pound box is normally distributed with a mean of 566 and a standard deviation of 33.
What is the probability that there are less than 500 nails in a randomly-selected five-pound box of nails? (express as a decimal, not a percentage)
P ( X < 500) = P( z < (500-566)/33) = P ( z z1 ) = .99
Z1 will be 2.326
So
QUESTION 24
QUESTION 25
Candidates for employment at a city fire department are required to
The area under the curve to the left of the unknown quantity must be 0.7 (70%). So, we must first find the z value that cuts off an area of 0.7 in the left tail of standard normal distribution. Using the cumulative probability table, we see that z=0.53.
2. In order to determine the average amount spent in November on Amazon.com a random sample of 144 Amazon accounts were selected. The sample mean amount spent in November was $250 with a standard deviation of $25. Assuming that the population standard deviation is unknown, what is a 95% confidence interval for the population mean amount spent on Amazon.com in November?
You work in marketing for a company that produces work boots. Quality control has sent you a memo detailing the length of time before the boots wear out under heavy use. They find that the boots wear out in an average of 208 days, but the exact amount of time varies, following a normal distribution with a standard
(a) Then mean of the sample and the value of Z with an area of 10% in right tail.
5. Give the standard deviation for the mean and median column. Compare these and be sure to identify which has the least variability?
Compute the population mean margin of error for a 90% confidence interval when sigma is 7 and the sample size is 36.
5. Give the standard deviation for the mean and median column. Compare these and be sure to identify which has the least variability?
2. For the following set of scores, fill in the cells. The mean is 74.13 and the standard deviation is 9.98.
5) Threat of substitutes is low, in comparison with technology that constantly evolves, furniture cannot be easily substituted. But its insignificant impact is fully neutralized by high competition problem.
The worksheet “Insurance” in the Excel workbook MATH302_Midterm.xls, which is attached, contains data on the percentage of people without health insurance coverage. These data are based on samples taken in 2004 for the fifty states and the District of Columbia. Use these data to answer questions 1 through 4.On average, what percentage of the people in the fifty states and the District of Columbia does not have health insurance? Place your answer, rounded to 2 decimal places, in the blank. 14.15 Do not use a percent sign. For example, 17.76 would be a legitimate entry.
distribution with an average of 2 per 30 second period. What is the probability of having
Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of
Davidson Hardware stocks an expensive composite-based plaster patching compound, currently classified “A” which is controlled by continuous review. Demand is variable, with an average of 6 pounds per week and a standard deviation of 2 pounds per week. Lead time is constant at one week. The firm’s current management of the product calls for a safety stock of one (1) pound.
28. The Polo Development Firm is building a shopping center. It has informed renters that their rental spaces will be ready for occupancy in 19 months. If the expected time until the shopping center is completed is estimated to be 14 months, with a standard deviation of 4 months, what is the probability that the renters will not be able to occupy in 19 months?
In this case, the extruder output should have a standard deviation of 1.667 thou. What proportion of the rubber extruded will be within specifications in this case?