Math Answers

In a study of the effects of early Alzheimer’s disease on nondeclarative memory, the Category Fluency Test to establish baseline persistence and semantic memory and language abilities. The eight subjects in the sample had Category Fluency Test scores of 11, 10, 6, 3, 11, 10, 9,11. Assume that the eight subjects constitute a simple random sample from a normally distributed population of similar subjects with early Alzheimer’s disease. (a) What is the point estimate of the population mean? (0.5) (b) What is the standard deviation of the sample? (1) (c) What is the estimated standard error of the sample mean? (0.5) (d) Construct a 90 percent confidence interval for the population mean category

if RS = 5x +6 ,ST=3x, and RT=30,find RS

A new car is purchased for 20700 dollars. The value of the car depreciates at 13.75% per year. What will the value of the car be, to the nearest cent, after 12 years?

Nine out of every 100 people in the Philippines have Type B positive blood. If 8 people are chosen at random, what is the probability that less than 3 people have Type B blood?

1.    The manufacturer of a certain kind of light bulb claims that the lifetime of the bulb in hours, X can be modeled as a random quantity with PDF.

              fx(x)= {0, x<100

c/x², x>=100,

where c is a constant.

i.   What value must c take in order for this to define a valid PDF?

ii.  What is the probability that the bulb lasts no longer than 150 hours?

iii. Given that a bulb lasts longer than 150 hours, what is the probability that it lasts longer than 200 hours?

iv. Evaluate the cumulative distribution function.

1.   The number of calls coming into a hotel’s reservation center averages three per minute.

a. Find the probability that no calls will arrive in a given one-minute period.

b. Find the probability that at least two calls will arrive in a given one-minute period.

1.   Each sample of water has a 10% chance of containing a particular organic pollutant. Assume that the samples are independent with regard to the presence of the pollutant.

Let X =the number of samples that contain the pollutant in the next 18 samples analyzed. Then X is a binomial random variable with p = 0:10 and   n = 18.

i.  Find the probability that in the next 18 samples, exactly 2 contain the pollutant.

ii.  Find the probability that 3≤ X ≤ 5

iii. Find the probability that X ≥ 2

1.    Consider the random quantity X, with PDF

   fx(x) = {4/3(2x-x^2), 0<x<2
            0,         otherwise. 

i.                  Check that this is a valid PDF (it integrates to 1).

ii.                Calculate the expectation and variance of X.

iii.              Evaluate the cumulative distribution function.

iv.               What is the median of this distribution? 

In a class of 28 students, 16 play an instrument and 11 play a sport. There are 7 students who do not play an instrument or a sport. What is the probability that a student plays an instrument given that they play a sport?

In a class of 28 students, 16 play an instrument and 11 play a sport. There are 7 students who do not play an instrument or a sport. What is the probability that a student plays an instrument given that they play a sport?