### FINAL EXAM STATISTICS

** FINAL EXAM STATISTICS **

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**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 the Distribution Table for X**

**b) Construct Probability Histogram**

**2) 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**

**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**

**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**

**f) 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?**

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

**a) Randomly chose an individual and calculate the probability that his/her 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 = 2**

**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)**