1. Let X represent the time, in minutes, for a clerk to process a certain type of application form. It takes a clerk between 4 and 6 minutes to process the application form. Suppose X is uniformly distrbuted between 4 and 6 minutes.

a.  Show the notation to describe the distribution of X.
b. What is the mean of X?
c.  Draw a uniform curve with parameters labeled.
d.  Shade and find P(4.57 < X < 5.5). 
e. Provide two interpretations of this area.
f. Shade and find P(X > 5.8)
g. Provide two interpretations of this area.

 

2. Consider the population of all 1-gal cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean (Mu) = 5 ml and standard deviation (Sigma) = 0.2 ml is a reasonable model for the distribution of the continuous random variable X = amount of red dye in the paint mixture.

a. Show the notation to discribe the distribution of X
b. Draw the normal cuve with parameter values labeled (include associated z-scores)
c. Find P(X<5.0) and interpret this area in two ways. Show all notation and calculator syntax (include a curve with shading)
d. Find the associated z score for x = 5.0.
e. Find P(X<5.4) and interpret this area in two ways. Show all notation and calculator syntax (include a curve with shading)
f. Find the associated z score for x = 5.4.
g. Find P(X>5.55) Show all notation and calculator syntax (include a curve with shading)
h. Find the associated z score for x = 5.55.
i. Find P( 4.85<X<5.31)Show all notation and calculator syntax (include a curve with shading)
j. Find the associated z scores for x = 4.85 and x = 5.31
k. Find P(X<4.0) Show all notation and calculator syntax (include a curve with shading)
l. Find the associated z score for x = 4.0.
m. What is the probability that the amount of red dye in the paint mixture is within 1.5 standard deviationd of the mean? Show all notation and calculator syntax (include a curve with shading)
n. What is the 75th percentile of red dye in the paint mixture? Show all notation, work and calculator syntax (include a curve with shading)
o. What amounts of red dye in the paint mixture represent the middle 40%? Show all notation, work and calculator syntax (include a curve with shading)
p. What amount of red dye in the paint mixture would be considered the cut-off for unusually high amounts. In other words, the amount of red dye that represents the TOP 5% of amounts. Show all notation, work and calculator syntax (include a curve with shading)