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FINAL EXAM

Summer 2020)

 

1) Take out two balls randomly, without replacement out of a box containing 4 white and 6 black balls. Let X be the number of white balls

 

a) Construct a Distribution Table for X

 

b) Construct Probability Histogram

 

 

2) Flip a coin twice. Let X be the number of heads. Calculate the expected value (the mean of X) and also the standard deviation of X

 

3) Real estate agent has a 30% chance of selling a house. Tomorrow the agent will show 4 houses.

a) Calculate the probability of selling at least 1 house.

b) How many houses does he expect to sell (when he shows 4 houses)?

 

c) What is the standard deviation of the random variable X, the number of successful house sales?

4) A random sample of 28 students’ final exam scores in Statistics is given below

0, 45,60,30,50,75,75,90,25,50,30,20,80,95,95,90,90,100,55,60,65,70,70,70,70,70,85,60

(Problems a – g refer to the above numbers.)

 

a) Construct a relative frequency table with classes of width 10

 

b) Construct a relative frequency histogram and comment on its shape. Can you tell, without any computation whether the mean is smaller/larger than the median, just based on the shape of the histogram?

 

 

c) Construct the box plot

 

 

 

 

 

d) Use the IQR test to check whether the score x = 0 is a left outlier

 

e) Find the population z – score for the score x = 50

mean=63.39286, sd=25.16809

 

 

g) The instructor feels that the average score on the statics exams (for all of students) is less than a C (C is 70%). Test his hypothesis at the 5% significance level based on the random sample of 28 students. Assume that the population standard deviation is sigma = 20

 

 

5) A Statistics professor wants to find out if the mean score on her test is more than 55. The usual population standard deviation on her tests is 20. She takes a random sample of 25 students and calculates the average to be 60. Test the appropriate hypothesis at the 5% significance level?

Hypothesis

 

6) IQ scores are normally distributed with mean 100 and standard deviation 16

a) Randomly chose an individual and calculate the probability that his IQ is more than 110

 

b) Calculate the probability that a random sample of size n = 25 produces a mean which is more than 110.

 

7) Consider the bivariate data {(2,5), (1,3), (5,6), (0,2)} where x is the number of miles and y is the number of dollars spent.

 

a) Write the equation of the regression line and draw it together with the scatter plot of the data

 

 

b) Find the predicted value for x = 3

 

c) Find the residual for x =

 

8)

In 2000 it was observed that 55% of professors were assistant professors, 36% were associate professors and (the rest 9%) were full professors. We want to find out if things have changed. We take a sample of 150 professors and find that 75 are assistants, 60 are associates and 15 are full. Test, at the 5% significance level if the two distributions fit together (if things have changed)