Find the probability that a randomly selected patient

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Assignment -

LEARNING UNIT HOMEWORK - THE NORMAL PROBABILITY DISTRIBUTION

Read Chapter 4 'Probability Distributions'.

Review the instructor's prompt 'Zscores' and the breeze presentation.

Review carefully the applications on the normal probability distribution, examined.

Do the following problems after reading the text and reviewing the prompt.

Application 1 - One of the variables collected in the North Carolina Birth Registry data (A-3) is pounds gained during pregnancy. According to data from the entire registry for 2001, the number of pounds gained during pregnancy was approximately normally distributed with a mean of 30.23 pounds and a standard deviation of 13.84 pounds. Calculate the probability that a randomly selected mother in North Carolina in 2001 gained:

a) Less than 15 pounds during pregnancy

b) More than 40 pounds

c) Between 14 and 40 pounds

d) Less than 10 pounds

e) Between 10 and 20 pounds

Application 2 - Suppose the average length of stay in a chronic disease hospital of a certain type of patient is 60 days with a standard deviation of 15. If it is reasonable to assume an approximately normal distribution of length of stay, find the probability that a randomly selected patient from this group will have a length of stay:

a) Greater than 50 days

b) Less than 30 days

c) Between 30 and 60 days

d) Greater than 90 days

Application 3 - If the total cholesterol values for a certain population are approximately normally distributed with a mean of 200 mg/100 ml and a standard deviation of 20 mg/100 ml, find the probability that an individual picked at random from this population will have a cholesterol value:

a) Between 180 and 200 mg/100ml

b) Greater than 225 mg/100 ml

c) Less than 150 mg/100 ml

d) Between 190 and 210 mg/100 ml

Application 4 - Given the normally distributed random variable X with mean 100 and standard deviation 15, find the numerical value of k such that:

a) P(X ≤ k) = .0094

b) P(X ≥ k) = .1093

c) P(100 ≤ X ≤ k) = .4778

d). P(k' ≤ X ≤ k) = .9660, where k' and k are equidistant from μ

Application 5 - a. Given the normally distributed random variable x, find the numerical value of k such that P(μ - kσ ≤ x ≤ μ + kσ)= .754

b. Given the normally distributed random variable x with σ = 10 and P(x ≤ 40) = .0080, find μ.

c. Given the normally distributed random variable x with σ = 15 and P(x ≤ 50) = .9904, find μ.

Application 6 - a. Given the normally distributed random variable x with σ = 5 and P(x ≥ 25) = .0526 find μ.

b. Given the normally distributed random variable x with μ = 25 and P(x ≤ 10) = .0778 find σ.

c. Given the normally distributed random variable x with μ = 30 and P(x ≤ 50) = .9772 find σ.

PROJECT - A research performed in hospitals analyzed the times it takes the hospital staff on average to complete non-emergency responses. The research found that the times required to complete a certain task was normally distributed, with a mean of 10 minutes and a standard deviation of 3 minutes. Are you able to determine the proportion of hospital staff completing the task in less than 4 minutes, the proportion of staff completing the task in more than 5 minutes, the proportion of staff completing the task within 3 minutes? Why or why not may these requests be answered in an accurate manner?

Attachment:- Assignment Files.rar

Reference no: EM132271530

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Instructions: Consider the following statements: "Eating fish may help to reduce your cholesterol"; "Taking calcium will lower blood pressure in some people"; "Studies suggest that using our exercise machines will reduce your weight". What makes these claims correct or incorrect? Please explain (answer in at least one paragraph). All math should be shown like this example application. For a grade level A: Attach the text and data of the research. You must provide your answers with all the applicable computations, formatted as word.doc using equation editor. You must answer the question(s) raised by this research. Each answer must be complete and correct.

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