Each sweat shop worker at a computer factory can put together 4.4 computers per hour on average with a standard deviation of 0.8 computers. 11 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected worker is observed, find the probability that this worker will put together between 4 and 4.2 computers per hour.
5. For the 11 workers, find the probability that their average number of computers put together per hour is between 4 and 4.2.
6. Find the probability that a 11 person shift will put together between 45.1 and 47.3 computers per hour.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. A sticker that says "Great Dedication" will be given to the groups of 11 workers who have the top 15% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)

The number of raisins in a 24 oz. box of Raisin Bran Cereal is normally distributed with a mean of 100 raisins and a standard deviation of 15 raisins.

1. What is the probability that a box of cereal will have no more than 110 raisins in it?
   1. 0
   2. 0.75
   3. 0.68
   4. 0.83

2. What is the probability that a box of cereal will have between 80 to 120 raisins?
   1. 0.5
   2. 0.32
   3. 0.67
   4. 0.82

3. Help the manager decide the raisin count per box for the top 3% boxes with respect to the raisin content. In other words, how many raisins must be in a box so that the box is in the top 3% with respect to raisin content? Pick the answer that comes closest to the correct answer.
   1. More than 106
   2. More than 112
   3. More than 128
   4. More than 142

4. Assume the manager wants 0.9 probability that a box of cereal has 60 or more raisins. Also assume that the process remains normally distributed and the standard deviation of process remains the same (i.e., 15 raisins). What should be the mean of the number of raisins in a box of cereal? Round off to nearest integer.
   1. 79
   2. 85
   3. 95
   4. 105

The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest bulk cargo port in the world. The U.S. Army Corps of Engineers reports that the port handles a mean of 4.5 million tons of cargo per week.† Assume that the number of tons of cargo handled per week is normally distributed with a standard deviation of 0.89 million tons.

(a)

What is the probability that the port handles less than 5 million tons of cargo per week? (Round your answer to four decimal places.)

(b)

What is the probability that the port handles 3 or more million tons of cargo per week? (Round your answer to four decimal places.)

(c)

What is the probability that the port handles between 3 million and 4 million tons of cargo per week? (Round your answer to four decimal places.)

(d)

Assume that 87% of the time the port can handle the weekly cargo volume without extending operating hours. What is the number of tons of cargo per week that will require the port to extend its operating hours? (Round your answer to one decimal places.)

Each sweat shop worker at a computer factory can put together 4.2 computers per hour on average with a standard deviation of 1 computers. 15 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of X X ? X X ~ N(,) What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) What is the distribution of ∑ x ∑x ? ∑ x ∑x ~ N(,) If one randomly selected worker is observed, find the probability that this worker will put together between 4.3 and 4.5 computers per hour. For the 15 workers, find the probability that their average number of computers put together per hour is between 4.3 and 4.5. Find the probability that a 15 person shift will put together between 61.5 and 66 computers per hour. For part e) and f), is the assumption of normal necessary? YesNo A sticker that says "Great Dedication" will be given to the groups of 15 workers who have the top 15% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)

Each sweat shop worker at a computer factory can put together 4.5 computers per hour on average with a standard deviation of 0.8 computers. 8 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected worker is observed, find the probability that this worker will put together between 4.6 and 4.7 computers per hour.
5. For the 8 workers, find the probability that their average number of computers put together per hour is between 4.6 and 4.7.
6. Find the probability that a 8 person shift will put together between 33.6 and 36.8 computers per hour.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. A sticker that says "Great Dedication" will be given to the groups of 8 workers who have the top 15% productivity. What is the least total number of computers produced by a group that receives a sticker? minutes (round to the nearest computer)

the results of a survey in which people from high income countries were asked to report their level of education (less than basic, basic and advanced) and whether they were employed or not. The results are in thousands and are for the 2016-17 period.

You work for a Human Resources firm interested in global employment trends. You randomly sample 30 employed people from high income countries and ask them about their level of education.

a) What is the probability that 24 or fewer of these people would have an advanced education? (Round to 3 decimals)

b) What is the probability that 3 or more of these people would have a less than basic education? (Round to 4 decimals)

c) What is the probability that at least 10 of these people would have a basic education? (Round to 2 decimals)

d) What's the expected number of employed people with a basic education (Round to the nearest integer)?

e) What does this data tell you about employment and education in high income countries?

When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Y denote the number of defective tires.

(a) If X and Y are independent with p_X(0) = 0.5, p_X(1) = 0.3, p_X(2) = 0.2, and p_Y(0) = 0.1, p_Y(1) = 0.2, p_Y(2) = p_Y(3) = 0.05, p_Y(4) = 0.6, display the joint pmf of (X, Y) in a joint probability table.

(b) Compute P(X ≤ 1 and Y ≤ 1) from the joint probability table.
P(X ≤ 1 and Y ≤ 1) =  

Does P(X ≤ 1 and Y ≤ 1) equal the product P(X ≤ 1) · P(Y ≤ 1)?

YesNo    

(c) What is P(X + Y = 0) (the probability of no violations)?
P(X + Y = 0) =  

(d) Compute P(X + Y ≤ 1).
P(X + Y ≤ 1) =

John Smith ran 50 simulations. Each of these represent a week (7 days) of working with a printing machine. During each simulation, the average number of the machine's failures per day was recorded. You observed that the mean of all of your sample means follows a normal distribution with a standard deviation of 25 that is, ~N(M, 25). Later you decided to run a hypothesis testing on the population mean with the assumptions below and an alpha = 0.01.

H0:The population mean is equal to 12

H1:The population mean is not equal to 12

What would be the lowest and highest values of the sample mean that would allow you to not reject the null hypothesis?

a) Lowest value:

b) Higherst value:

The price of shares of the Continental Bank at the end of trading each day for the last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $42.00 per share and the standard deviation was $2.25 per share. Refer to the table in Appendix B.1. (Round the final answers to 2 decimal places.)  

a-1. What percentage of the days was the price over $45.00?

Percentage of days ________ %

a-2. How many days would you estimate?

Number of days ______

b. What percentage of the days was the price between $38.00 and $40.00?

Percentage of days _______ %

c. What was the minimum price of the stock on the highest 15 days of the year?

Stocks price ________ $

------An analog signal is sampled, quantized, and encoded into a binary PCM wave. The number of representation levels used is 1024. A synchronizing pulse is added at the end of each code word representing a sample of the analog signal. The resulting PCM wave is transmitted over a channel of bandwidth 24kHz using a 8 PAM system with raised-cosine spectrum. The rolloff factor is 0.5.

(a) Find the rate (bit/s) at which information is transmitted through the channel.

(b) Find the rate at which the analog signal is sampled. What is the maximum possible value for the highest frequency component of the analog signal?

is using a 8 PAM system is different from using a quaternary PAM in this example ?????

thanks