Probability distribution

Please annotate steps when solving the attached problems. I would like to use them as a reference.

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The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds.
a. What is the area between 415 pounds and the mean of 400 pounds?
b. What is the area between the mean and 395 pounds?
c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?

The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution.
a. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect?
b. What percent of the garages take between 29 hours and 34 hours to erect?
c. What percent of the garages take 28.7 hours or less to erect?
d. Of the garages, 5 percent take how many hours or more to erect?

A study of absenteeism from the classroom is being conducted. In terms of statistics, the study is called:
a. An experiment
b. An event
c. An outcome
d. A joint probability

To apply this rule of addition, P(A or B or C) _ P(A) _ P(B) _ P(C), the events must be
a. Joint events
b. Conditional events
c. Mutually exclusive events
d. Independent events

Management claims that the probability of a defective relay is only 0.001. The probability of the relay not being defective is
a. 0.002
b. 0.000001
c. 0.999
d. 1.0

The binomial and Poisson probability distributions are
a. Continuous
b. Either discrete or continuous
c. Discrete
d. Normal

A uniform probability distribution is
a. Symmetric around the mean
b. Bell shaped
c. Asymptotic to the X-axis
d. All of the above

If we use z scores to convert any normal distribution, the new distribution is
a. A binomial distribution with mean 0 and standard deviation _
b. A standard normal distribution with a mean of 0 and standard deviation of 1
c. A standard normal distribution with a mean of _ and variance _2
d. A Poisson distribution with mean 0

Urban Plastic Products, Inc. is concerned about the inside diameter of the plastic PVC pipe it produces. A Machine extrudes the pipe, which is then cut into 10-foot lengths. About 720 pipes are produced per machine during a two-hour period. How would you go about taking a sample from the two-hour production period?

A state meat inspector in Iowa has been given the assignment of estimating the mean net weight of packages of ground chuck labeled "3 pounds." Of course, he realizes that the weights cannot be precisely 3 pounds. A sample of
36 packages reveal the mean weight to be 3.01 pounds, with a standard deviation of 0.03 pounds.
a. What is the estimated population mean?
b. Determine a 95 percent confidence interval for the population mean.

The Human Relations Department of Electronics, Inc., would like to include a dental plan as part of the benefits package. The question is: How much does a typical employee and his or her family spends per year on dental expenses? A sample of 45 employees reveals the mean amount spent last year was $1,820, with a standard deviation of $660.
a. Construct a 95 percent confidence interval for the population mean.
b. The information from part (a) was given to the president of Electronics, Inc. He indicated he could afford $1,700 of dental expenses per employee. Is it possible that the population mean could be $1,700? Justify your answer.

Dole Pineapple, Inc. is concerned that the 16-ounce can of sliced pineapple is being overfilled.
The quality-control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces, with a sample standard deviation of 0.03 ounces. At the 5 percent level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p-value.