What two properties must be satisfied by a continuous probability distribution / probability curve?

Business Statistics – Week 4 Assignment 2

Week 4 Assignment

1.     What two properties must be satisfied by a continuous probability distribution / probability curve?

(If you use f(x) in your definition you must explain what this notation means and what a function is).

2.    Explain what the mean µ tells us about a normal curve, and explain what the standard deviation σ tells us about a normal curve. Explain in at least a paragraph.

3.    Explain how to compute the z value. What does the z value tell us about the value of the random variable?

4.    Let x be a normally distributed random variable with µ=90 and σ=12. Find the z value for each of the following observed values of x:

a.    X = 42

b.    X = 60

c.     X = 75

d.    X = 99

e.    X = 120

f. Which value above is unrealistic when we are referring to a normal curve?  Why?

5.    If the random variable z has a standard normal distribution, sketch and find each of the following probabilities. Use https://onlinestatbook.com/2/calculators/normal_dist.html.

   Take screenshots of the curve and include these or draw the respective shaded areas and include in your document.

a. P(1.72 <z < 1.98)

b. P( – 2.17< z  < 0.71)

c. P(z > 1.77)

d. P(z<2.37)

6.    Take screenshots of the curve and include these or draw the respective shaded areas and include in your document.

The average number of years a person takes to complete a graduate degree program is 3. The standard deviation is 4 months. Assume the variable is normally distributed. If an individual enrolls in the program, find the probability that it will take

a. More than 4 years to complete the program

b. Less than 3 years to complete the program

c. Between 3.8 and 4.5 years to complete the program

7. The Central Limit Theorem is one of the most important theorems in Statistics. What does it tell us about the sampling distribution and sample mean?

8. Use the CLT to solve this problem AND show your work:

A recent study of the life span of portable compact disc players found the average to be 3.7 years with a standard deviation of 0.6 year. If a random sample of 32 people who own CD players is selected,

a) find the probability that the mean lifetime of the sample will be less than 3.4 years.

b)  If the mean is less than 3.4 years, would you consider that 3.7 years might be incorrect?

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