Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 45 and standard deviation σ = 14. Find the following probabilities. (Round your answers to four decimal places.)

(a) x is less than 60


(b) x is greater than 16


(c) x is between 16 and 60


(d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

Show that the skewness of X~Poisson(λ) is λ^-(1/2)

Please give a step by step solution:

The ages of a group of 50 women are approximately normally distributed with a mean of 50 years and a standard deviation of 55 years. One woman is randomly selected from the​ group, and her age is observed.

a. Find the probability that her age will fall between 56 and 59years.

b. Find the probability that her age will fall between 4747 and 51 years.

c. Find the probability that her age will be less than 35 years.

d. Find the probability that her age will exceed 41 years.

Suppose x has a distribution with μ = 65 and σ = 9.

(a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?

No, the sample size is too small.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 9.     Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 0.6.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 2.25.

(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?

No, the sample size is too small.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 2.25.     Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 9.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 0.6.

Find P(61 ≤ x ≤ 66). (Round your answer to four decimal places.)

Let the continuous random variable X have probability density function f(x) and cumulative distribution function F(x). Explain the following issues using diagram (Graphs)

a) Relationship between f(x) and F(x) for a continuous variable,

b) explaining how a uniform random variable can be used to simulate X via the cumulative distribution function of X, or

c) explaining the effect of transformation on a discrete and/or continuous random variable

Assume that a driver faces the following loss distribution:

Loss 10,000 0

Probability .04 .96

These two drivers decide to pool their losses with two other drivers with the same loss distribution, and all losses are not correlated, i.e., independent.

6. What is the expected loss for each member of the pool?
7. What is the standard deviation of loss for each member of the pool?

Now consider another group of four drivers who have formed a separate pool, and who each have this loss distribution( before pooling):

Loss
15,000 10,000 0

Probability

.01 .05 .94

8. What is the expected loss for each member of this new pool of four drivers (after pooling)?

9. What is the standard deviation of loss for each member of this new pool (after pooling)?

10. If all 8 drivers decide to pool their risks, what would the expected loss for each member of this pool of eight drivers be?

In the EAI sampling problem, the population mean is $51,800 and the population standard deviation is $4,000. When the sample size is n = 20, there is a 0.4246 probability of obtaining a sample mean within +/-$500 of the population mean. Use z-table.

a. What is the probability that the sample mean is within $500 of the population mean if a sample of size 40 is used (to 4 decimals)?

b. What is the probability that the sample mean is within $500 of the population mean if a sample of size 80 is used (to 4 decimals)?

It is known that the thread life of a certain type of tire has a normal distribution with standard deviation of 1500.

a) A sample of 16 tires is found to have an average thread life of 30960. Does this provide sufficient evidence at 1% level of significance to conclude that the true average thread life of this type of tires is more than 30000? Explain by carrying out an appropriate hypothesis test stating clearly the hypotheses.

b) What is the probability of making a Type II error in the hypothesis test in part "a" if the true average thread life is in fact 31000?

c) If a 1% level of significance is used to carry out the test in part "a" and it is also required that ?(30500) = 0.05, what sample size is necessary?

THE ANSWERS ARE AS FOLLOWS

a) ?=30000, ?>30000, z=2.56, z0.01=2.327, reject.

b) 0.3671

c) 142

Please explain the process to solve this problem. Thank you!

Your leader wants you to evaluate the difference in cycle time between three different offices. Describe the steps you would take in the evaluation in order to provide a report so the leader can take action. In replies to peers, indicate whether you agree or disagree with the steps they outlined. Justify your response using what you learned from the topic materials.

In your own words, describe the difference between Among Group Variation and Within Group Variation. Discuss how you would evaluate the variation and other methods to ensure that the data is appropriate to use for the test. Illustrate using a specific example.

1a. Suppose I have a gaming web site that can only handle 10 players at the same time, or else my server will crash. I have 50 users. Each user is online and playing the game 20% of the time. What is the probability that my server will crash. 1b Now suppose that it is acceptable if the crashing probability is less than 1%. What is the maximum number of users my server can handle? 1c. What is the maximum number of users I can support if my server is twice as large and can handle 20 simultaneous players?

A weekly time ticket for Joyce Caldwell follows:    

Required:
Prepare a journal entry to record Joyce’s wages. (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field.)

     

A large school district claims that 80% of the children are from low-income families. 130 children from the district are chosen to participate in a community project. Of the 130 only 72% are from low-income families. The children were supposed to be randomly selected. Do you think they really were?

a. The null hypothesis is that the children were randomly chosen. This translates into drawing times

at random
with replacement
without replacement

from a null box that contains

b.
130 tickets, 72% marked "1" and 28% marked "0"
Thousands of tickets, 80% marked "1" and 20% marked "0"
Thousands of tickets marked either "1" or "0", but the exact percentages of each are unknown and estimated from our sample.
5 tickets, 1 marked "1" and 4 marked "0"

c. What is the expected value of the percent of 1's in the draws? (Don't type in the % sign)

%

d. What is the SD of the null box? (Note: We don't have to estimate the SD of the box from the sample SD because we can compute it directly from the percent of 1's in the null box. This is why we never use a t-test for problems that can be translated into 0-1 boxes.)

e. What is the standard error of the % of 1's in the draws? (Round to 2 decimal places.) %

f. What is the value of the test statistic z? (Round answer to 2 decimal places.)

g. What is the p-value? Click here to view the normal table
%

h. What do you conclude?
There is very strong evidence to reject the null, and conclude that the children were not randomly chosen.
We cannot reject the null, it's plausible the children were randomly chosen.

Danielle and William are visiting an ice cream shop where they will randomly choose one of the following five regular and premium flavors.

Flavors Price

Vanilla Bean $2.00

Chocolate Mint $3.00

Pralines and Cream $4.00

Strawberry Shortcake $5.00

Fudge Brownie Caramel Cheesecake Deluxe $6.00

Define the population as the five services and a sample of size two as the flavor that Danielle chooses and the service that William chooses.

a. Identify the frequency distribution for the population

b. Identify the frequency distribution for all combinations of samples means for Danielle and William choosing a flavor

c. Verify that the population mean and man of all possible sample means are equal

d. Calculate the standard error.

Suppose you know that the amount of time it takes your friend Susan to get from her residence to class averages  50 minutes, with a standard deviation of 55 minutes. What proportion of Susan's trips to class would take more than  50 minutes? . Enter your answers accurate to two decimal places.

What proportion of her class would take more than  50 minutes?

What proportion of Susan's trips to class would take less than 40 minutes?

What proportion of Susan's trips to class would take more than  50 minutes or less than  40 minutes?