Statistics and Probability Answers

At the town fair, you can pay $5 to toss a ring at a set of bottles. If you get a “ringer” on the small mouth bottle, you win $35. If you get a “ringer” on the medium bottle, you win $10. If you get a “ringer” on the large bottle, you get your $5 fee back (that is, you break even). If you miss, you are out the $5 you paid to play. Ryan is a good shot and his probability of getting a ringer on the small, medium, and large bottles is 10%, 10%, and 5%, respectively.
X -$5 $0 $10 $35
P 0.75 0.10 0.10 0.05
a. Find the math expectation of Ryan’s winnings for a single game.
b. Find the math expectation of Ryan’s winnings after 5 games.
c. Find the variance of Ryan’s winnings for a single game.
d. Find the standard deviation of Ryan’s winnings for a single game.
e. Does it pay for Ryan to play this game at the fair?
f. Find the cumulative distribution function of Ryan’s winnings for a single game and draw its graph.

A lawsuit has been brought by female managers of the company. Recently the company decided to promote three of the eight mid-level managers to top vice president positions. Of the mid-level managers, five for woma. Of the mid-level managers, five where woman and three were men, get all of the positions went to the men were woman and three were men, get all of the positions went to the men, . The lawyer for the woman believes that they have the case if the probability of only men getting these emotions by chance alone is less than 5%. Do the female employees have a case? Just the fire answer. The lawyer for the woman believes that they have the case if the probability of only men getting these through promotions by the chance alone is less than 5%. Do the female employees have a case? Justify your answer

sy=4
r=-0.6
b1x=2
bo=30
y=18

find x and sx

According to The World Bank, only 9% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 150 people in Uganda. Let X = the number of people who have access to electricity.
a. What is the probability distribution for X?
b. Using the formulas, calculate the mean and standard deviation of X.
c. Use your calculator to find the probability that 15 people in the sample have access to electricity.
d. Find the probability that at most ten people in the sample have access to electricity.
e. Find the probability that more than 25 people in the sample have access to electricity.

Wildlife researchers monitor many wildlife populations by taking aerial photographs. can they estimate the weight of alligators accurately from the air?
dependent variable is weight
R^2 = 83.6%
s=54.01

intercept(variable) -393(coefficient) 47.53(SE Coeff) -8.27(T ratio) <0.0001(p value)
Length(variable) 5.9(coefficient) 0.5448(SE Coeff) 10.8 (t ratio) <0.0001 (p value)

a) did they chose the correct variable to use as the dependent variable and the predictor? explain
b)what is the correlation between an alligators length and weight
c) write the regression equation
d) interpret the slope of the equation in this context

suppose the entering freshman at a certain college have mean combined SAT scores of 1222, with a standard deviation of 123. in the first semester these students attained a mean GPA of 2.66 with a standard deviation of 0.56. a scatterplot showed the association to be reasonably linear, and the correlation between SAT and GPA was 0.47

a) write the equation of the regression line
b) explain what the y-intercept of the regression line indicates
c) interpret the slope of the regression line
d) predict the GPA of a freshman who scored a combined 1400
e) based upon these statistics how effective do you think SAT scored would be in predicting academic success during the first semester of the freshman year at this college? explain
f) as a student would you rather have a positive or negative residual in this context? explain

The correlation r= -0.86 the mean mortgage amount is $121.8 thousand and the mean interest rate is 7.74. the standard deviations are $47.36 thousand for mortgage amounts and 1.79% for interest rates
a) is the regression model appropriate for predicting mortgage amount from interest rates? explain
b) what is the equation that predicts mortgage amount from interest rates
c) what would you predict the mortgage amount would be if the interest rates climbed to 13%
d) do you have any reservations about your prediction in part C

dependent variable is home attendance
r-squared= 28.4%
variable is coefficient
constant= -6760.5
wins= 431.22

a) write a equation of the regression line
b) estimate the average attendance for a team with 50 wins
c) interpret the meaning of the slope of the regression line in this context
d) in general what would a negative residual mean in this context
e) the giants won 92 games and averaged 41,736 fans at their home games. calculate the residual for this team and explain what it means

dependent variable is home attendance
r-squared= 28.4%
variable is coefficient
constant= -6760.5
wins= 431.22

a) do you think a linear model is appropriate here?
b) interpret the meaning of r^2 in the context

consider the roller coasters described in exercise 30 again. The regression analysis gives the model duration= 64.232+0.180 drop
a) explain what the slope of the line says about how long a roller coaster ride may last and the height of the coaster
b) a new roller coaster advertises and initial drop of 200 feet. how long would you predict the ride lasts
c) another coaster with 50 foot initial drop advertises a 2 minute ride. is it longer or shorter than you would expect? by how much? whats that called?