Statistics and Probability Answers

store manager claims that the average age of his customers is less than 40 years old, while the industry average is 40 years old. He asks you to test his thinking. You collect a sample of 50 customers and found that the average age is 38.7. Assuming that the population standard deviation is 12.5 years and using α = 0.05, test your manager's hypothesis. What is your conclusion?
H0
μ = 40
H1
μ < 40

Find the moment generating function of random variable which is uniformly distributed over
(–a, a). Evaluate E (X2n).

Suppose a baker claims that the mean time to prepare a cake is at most 360 minutes. A sample of 25 bakers in randomly selected and it is found that the mean time taken by them to prepare a cake was 270 minutes. Assume also that standard deviation is known to be 120 minutes. Assuming the time to prepare a cake is normally distributed and using a 0.05 level of significance, would you conclude the baker’s claim is true?

if n=10 and pie=0.70 then the standard deviation of the binomial distribution is

if we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot.

At a university, the average cost of books per student has been $400 per student per semester. The Dean of Students believes that the costs are increasing and that the average is now greater than $400. He surveys a sample of 40 students and finds that for the most recent semester their average cost was $430 with a standard deviation of $80. What is the test value for this hypothesis test?

body temp is normally distributed. Average temp is 98.2 with a standard deviation of 0.7.
suppose that nurse takes the body temp of 10 patients. What is the probability that at least two of the patients have body temps that exceed 98.6.

Im not sure if I use poisson formula or normal distribution formula. Any advice would be great

4. By the method of least squares, fit a straight line for the following data:

x 1 2 3 4 5
y 14 13 9 5 2



5. Write a c++ program to find the sum of 0.123  103 and 0.456  102 and write the result in three significant digits.

6. Find the moment generating function of random variable which is uniformly distributed over

(–a, a). Evaluate E (X2n).

How do I calculate distribution of scores when x=75, std = 6.38 what is probability of score falling between a raw score of 70 and 80.

if f(x)=a raise to x,a>0,show that
f(x+1)=a*f(x)=f(2)*f(x-1)