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Statistics and Probability
A person must pay 9$ to play a certain game at the casino. Each player has a probability of 0.11 of winning 15$, for a net gain of 6 (the net gain is the amount won 15$ minus the cost of playing 9$).
Each player has a probability of 0.89 of losing the game, for a net loss of 9 (the net loss is simply the cost of playing since nothing else is lost).
What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places.
Expected Value = $
If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind?
ahead
behind
Statistics and Probability
Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $5. If Kyd selects any other type of card, he pays North $2.
a) What is Kyd's expected value for this game? Round your answer to the nearest cent. $
b) What is North's expected value for this game? Round your answer to the nearest cent. $
c) Who has the advantage in this game?
a) What is Kyd's expected value for this game? Round your answer to the nearest cent. $
b) What is North's expected value for this game? Round your answer to the nearest cent. $
c) Who has the advantage in this game?
Statistics and Probability
In a lottery game, a player picks six numbers from 1 to 27. If the player matches all six numbers, they win 50,000 dollars. Otherwise, they lose $1.
What is the expected value of this game? $
What is the expected value of this game? $
Statistics and Probability
A quick quiz consists of a multiple-choice question with 6 possible answers followed by a multiple-choice question with 3 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
Statistics and Probability
jar contains 10 red marbles numbered 1 to 10 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability of the given event.
(a) The marble is red
Your answer is :
(b) The marble is odd-numbered
Your answer is :
(c) The marble is red or odd-numbered
Your answer is :
(d) The marble is blue or even-numbered
Your answer is :
(a) The marble is red
Your answer is :
(b) The marble is odd-numbered
Your answer is :
(c) The marble is red or odd-numbered
Your answer is :
(d) The marble is blue or even-numbered
Your answer is :
Statistics and Probability
A company estimates that 0.2% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $150.
If they offer a 2 year extended warranty for $9, what is the company's expected value of each warranty sold?
If they offer a 2 year extended warranty for $9, what is the company's expected value of each warranty sold?
Statistics and Probability
A random sample of 8 cigarettes of a certain brand
Statistics and Probability
The life of a 60- watt light bulb in hours is known to be normally distributed with σ = 25
hours. Create 5 different random samples of 100 bulbs each which has a mean life of x_bar ~
1000 hours and perform one-way ANOVA with state it.
hours. Create 5 different random samples of 100 bulbs each which has a mean life of x_bar ~
1000 hours and perform one-way ANOVA with state it.
Statistics and Probability
On the basis of the following data, the marketing manager wants to predict the sales
volume for the locality on the basis of # households, number of cars and marketing
expense
Sl.No. Sales Volume #Households number of cars marketing expense
1 15727 161 3 180
2 9328 99 1 150
3 13681 135 2 175
4 12379 120 2 165
5 15351 164 3 178
6 24174 221 5 220
7 20154 179 4 205
8 20671 204 5 210
9 22978 214 5 128
10 13522 101 1 176
11 22471 231 5 226
12 19529 206 4 296
13 24216 248 3 240
14 11521 107 2 168
15 197.82 205 3 100
i. Draw three scatter plots of sales volume with each of the three variables and comment
on their correlation.
ii. Regress the sales volume on #household, number of cars and marketing expense.
Calculate R square and interpret the same.
iii. Determine which variable is/are significant variable/s. Is there any insignificant
variable? If yes, regress again, by dropping the variable. Will dropping that variable
increases the adjusted R square?
volume for the locality on the basis of # households, number of cars and marketing
expense
Sl.No. Sales Volume #Households number of cars marketing expense
1 15727 161 3 180
2 9328 99 1 150
3 13681 135 2 175
4 12379 120 2 165
5 15351 164 3 178
6 24174 221 5 220
7 20154 179 4 205
8 20671 204 5 210
9 22978 214 5 128
10 13522 101 1 176
11 22471 231 5 226
12 19529 206 4 296
13 24216 248 3 240
14 11521 107 2 168
15 197.82 205 3 100
i. Draw three scatter plots of sales volume with each of the three variables and comment
on their correlation.
ii. Regress the sales volume on #household, number of cars and marketing expense.
Calculate R square and interpret the same.
iii. Determine which variable is/are significant variable/s. Is there any insignificant
variable? If yes, regress again, by dropping the variable. Will dropping that variable
increases the adjusted R square?
Statistics and Probability
A box of 12 transistors has 3 defective ones. If 2 transistors are drawn from the box together, what is the probability that
(I)both transistors are defective?
(II) neither transistor is defective?
(III)one transistor is defective?
(I)both transistors are defective?
(II) neither transistor is defective?
(III)one transistor is defective?
