1. Following table shows the probability distribution for the number of bathrooms for homes sold in the Goodyear, Arizona.

1. Compute the mean and the standard deviation of this distribution.

If a fair coin is tossed 25 times, the probability distribution for the number of heads, X, is given below. Find the mean and the standard deviation of the probability distribution using Excel

• Enter the mean and round the standard deviation to two decimal places.

x   P(x)
0   0
1   0
2   0
3   0.0001
4   0.0004
5   0.0016
6   0.0053
7   0.0143
8   0.0322
9   0.0609
10   0.0974
11   0.1328
12   0.155
13   0.155
14   0.1328
15   0.0974
16   0.0609
17   0.0322
18   0.0143
19   0.0053
20   0.0016
21   0.0004
22   0.0001
23   0
24   0
25   0

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 7 ounces.

a. The process standard deviation is 0.10, and the process control is set at plus or minus 2 standard deviation s . Units with weights less than 6.8 or greater than 7.2 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?

In a production run of 1000 parts, how many defects would be found (round to the nearest whole number)?

b. Through process design improvements, the process standard deviation can be reduced to 0.08. Assume the process control remains the same, with weights less than 6.8 or greater than 7.2 ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)?

In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?

What is the probability that the random variable X (which is the number of Heads from flipping a coin 5 times) is equal to 0?

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 14 ounces.

The process standard deviation is 0.2, and the process control is set at plus or minus 0.5 standard deviation. Units with weights less than 13.9 or greater than 14.1 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?


In a production run of 1000 parts, how many defects would be found (to 0 decimals)?

Through process design improvements, the process standard deviation can be reduced to 0.05. Assume the process control remains the same, with weights less than 13.9 or greater than 14.1 ounces being classified as defects. What is the probability of a defect (rounded to 4 decimals; getting the exact answer, although not necessary, will require Excel)?


In a production run of 1000 parts, how many defects would be found (to 0 decimals)?

What is the advantage of reducing process variation? SELECT A,B OR C

A.it can substantially reduce the number of defects

B.it may slightly reduce the number of defects

C.it has no effect

PLEASE SHOW YOUR WORK

Mean number of flights are 54 with a standard deviation of 13 What is the probability that the farmer will count 60 or fewer flights on average in the next 40 rows down? Round to four places

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the mean, variance, and standard deviation.

1. Given a randomly chosen 4-digit number...

What is the probability...

a. That there are no pairs of consecutive digits in the number

b. That there are no pairs of consecutive digits in the number, if the last digit and first digit of the number could be classified as consecutive

c. Given a randomly chosen six digit number:

What is the probability that the number is an odd number if it contains the six digits 7-6-4-4-3-1, and is in a random order?

First consider the following probability distribution for the total number of devices that connect to a home router.

X             p(x)

1             6%

2             4%         

3             2%

4             3%

5             4%

6             4%         

7             4%

8             5%

9             8%

10           10%

11           9%

12           8%

13           8%

14           6%

15           5%

16           4%

17           3%

18           3%

19           2%

20           2%

• Generate plots of the PDF and CDF for this distribution.
  • • Calculate the following o The expectation and the variance of the number of devices.
  • o The probability that a customer has 10 or fewer devices connecting.
  • o The probability that a customer has 14 or more devices connecting.
  • o The 50th percentile of the distribution.
  • • Now assume that the amount of data transferred per day is normally distributed with a mean of 15 GB and a standard deviation of 5 GB. Assume the data transferred each day is independent of other days. Calculate the following o The probability a customer transfers more than 18 GB in a day.
  • o The probability a customer transfers more than 18 GB for 3 days in a row.
  • o The 90th percentile of the daily transfer amount.

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 12 ounces.

a. The process standard deviation is 0.10 ounces, and the process control is set at plus or minus 1.75 standard deviations. Units with weights less than 11.825 or greater than 12.175 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?

In a production run of 1000 parts, how many defects would be found (round to the nearest whole number)?

b. Through process design improvements, the process standard deviation can be reduced to 0.06 ounces. Assume the process control remains the same, with weights less than 11.825 or greater than 12.175 ounces being classified as defects. What is the probability of a defect (round to 4 decimals; if necessary)?

In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?

c. What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard deviations from the mean?

a. it can substantially reduce the number of defects

b. it may slightly reduce the number of defects

c. it has no effect on the number of defects