A manufacturer of game controllers is concerned that its controller may be difficult for​ left-handed users. They set out to find lefties to test. About 11​%

of the population is​ left-handed. If they select a sample of 6 customers at random in their​ stores, what is the probability of each of the outcomes described in parts a through f​ below?

a. The first lefty is the sixth person chosen

b. There are some lefties among the 6 people

c. The first lefty is the second or third person

d. There are exactly 3 lefties in the group

e. There are at least 3 lefties in the group

f. There are no more than 3 lefties in the group

(round to four decimal places)

A marketing researcher wants to estimate the mean amount spent per year​ ($) on a web site by membership member shoppers. Suppose a random sample of 100 membership member shoppers who recently made a purchase on the web site yielded a mean amount spent of $57 and a standard deviation of ​$ 54 Complete parts​ (a) and​ (b) below.

a. Is there evidence that the population mean amount spent per year on the web site by membership member shoppers is different from %51 (Using a .01 level of significance)

Identify the critical​ value(s).

Determine the test statistic.

State the conclusion.

Determine the​ p-value and interpret its meaning

A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A1) = 0.10 P(A2) = 0.08 P(A3) = 0.06 P(A1 ∪ A2) = 0.12 P(A1 ∪ A3) = 0.13 P(A2 ∪ A3) = 0.12 P(A1 ∩ A2 ∩ A3) = 0.01 (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)

A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 40% of the time she travels on airline #1, 30% of the time on airline #2, and the remaining 30% of the time on airline #3. For airline #1, flights are late into D.C. 35% of the time and late into L.A. 25% of the time. For airline #2, these percentages are 35% and 20%, whereas for airline #3 the percentages are 15% and 10%. If we learn that on a particular trip she arrived late at exactly one of the two destinations, what are the posterior probabilities of having flown on airlines #1, #2, and #3? Assume that the chance of a late arrival in L.A. is unaffected by what happens on the flight to D.C. [Hint: From the tip of each first-generation branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.] (Round your answers to four decimal places.) airline #1 airline #2 airline #3

Consider the following information about travelers on vacation: 40% check work email, 30% use a cell phone to stay connected to work, 25% bring a laptop with them, 16% both check work email and use a cell phone to stay connected, and 44% neither check work email nor use a cell phone to stay connected nor bring a laptop. In addition, 88 out of every 100 who bring a laptop also check work email, and 70 out of every 100 who use a cell phone to stay connected also bring a laptop. (a) What is the probability that a randomly selected traveler who checks work email also uses a cell phone to stay connected? Incorrect: Your answer is incorrect. (b) What is the probability that someone who brings a laptop on vacation also uses a cell phone to stay connected? (c) If the randomly selected traveler checked work email and brought a laptop, what is the probability that he/she uses a cell phone to stay connected? (Round your answer to four decimal places.)

This problem is going to use the data set in R called "ChickWeight" that has 4 variables, as described below.

ChickWeight:
A data frame with 578 observations on 4 variables.
1) weight: a numeric vector giving the body weight of the chick (gm).
2) Time: a numeric vector giving the number of days since birth when the measurement was made.
3) Chick: an ordered factor with levels 18 < ... < 48 giving a unique identifier for the chick. The ordering of the levels groups chicks on the same diet together and orders them according to their final weight (lightest to heaviest) within diet.
4) Diet: a factor with levels 1, ..., 4 indicating which experimental diet the chick received.

Using a significance level of 0.05, is there evidence to support that the weight can be determined by the Time, Diet, and the interaction between the two? (Appears as Time:Diet in RStudio)

Fill in the R code below.

dat.aov = aov( ~ factor( ) *  , data= )
summary( )

Fill in the ANOVA table below.
Type the values into the table EXACTLY as they appear in your output in RStudio.

Is there evidence to support a significant interaction between Time and Diet?
1. ?0:H0: No AB interaction vs ??:Ha: Factors A and B interact
2. ?=0.05α=0.05
3. F =  
4. ??Fα =  
5. Conclusion:
Reject H0
Fail to reject H0
Interpretation:
There is sufficient evidence to support that the interaction between Time and Diet is significant.
There is not sufficient evidence to support that the interaction between Time and Diet is significant.

A defective car has a probability of 2/3 upon turning on the ignition in each attempt. Assume attempts

are independent.

• (a) What is the probability that exactly 3 attempts are needed until the car starts?

• (b) What is the probability that 3 or 4 attempts are needed?

• (c) What is the probability of success in 4 or more trials?

This problem is going to use the data set in R called "ChickWeight" that has 4 variables, as described below.

ChickWeight:
A data frame with 578 observations on 4 variables.
1) weight: a numeric vector giving the body weight of the chick (gm).
2) Time: a numeric vector giving the number of days since birth when the measurement was made.
3) Chick: an ordered factor with levels 18 < ... < 48 giving a unique identifier for the chick. The ordering of the levels groups chicks on the same diet together and orders them according to their final weight (lightest to heaviest) within diet.
4) Diet: a factor with levels 1, ..., 4 indicating which experimental diet the chick received.

Using a significance level of 0.05, is there evidence to support that the weight can be determined by the Time (treatment) and Diet (block)?

Fill in the R code below.

dat.aov=aov( ~ factor( ) +  ,data= )
summary( )

Fill in the ANOVA table below.
Type the values into the table EXACTLY as they appear in your output in R.

Is there evidence to support that the treatment variable Time is significant?
1. ?0:?1=?2=...=?12H0:μ1=μ2=...=μ12 vs ??:????Ha:ALOI
2. ?=0.01α=0.01
3. F =  
4. ??Fα =  
5. Conclusion:
Reject H0
Fail to reject H0
Interpretation:
There is sufficient evidence to support that the variable Time is significant.
There is not sufficient evidence to support that the variable Time is significant.

Is there evidence to support that the block variable Diet is significant?
1. ?0:H0: No block effect vs ??:Ha: There is a block effect
2. ?=0.01α=0.01
3. F =  
4. ??Fα =  
5. Conclusion:
Reject H0
Fail to reject H0
Interpretation:
There is sufficient evidence to support that the variable Diet is significant.
There is not sufficient evidence to support that the variable Diet is significant.

There are 6 purple balls, 5 blue balls, and 3 green balls in a box. 5 balls were randomly chosen (without replacing them). Find the probability that

(a) Exactly 3 blue balls were chosen.

(b) 2 purple balls, 1 blue ball, and 2 green balls were chosen.

1. STATISTICAL RESULTS: Report and statistically interpret the results with an appropriate tabular format and text. See the Output B. [6 pt]

2. DISCUSSION: Discuss what the results imply. [2 pt]

Output A. Descriptive statistics

Output B. Simple Linear Regression Results

Figure shows a contact lens table tht contains information about contact lens prescriptions (hard, soft and no contact lens) From the table derive quantitative association rules by mapping tables to Boolean association rules.

Prove Var(|X|) <= Var(X)

1. For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015. Assume the standard deviation is $3,540 and that debt amounts are normally distributed.

1. What is the probability that the debt for a borrower with good credit is more than $18,000?
2. What is the probability that the debt for a borrower with good credit is less than $10,000?
3. What is the probability that the debt for a borrower with good credit is between $12,000 and $18,000?
4. What is the probability that the debt for a borrower with good credit is no more than $14,000?

1. For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015. Assume the standard deviation is $3,540 and that debt amounts are normally distributed.

1. What is the probability that the debt for a borrower with good credit is more than $18,000?
2. What is the probability that the debt for a borrower with good credit is less than $10,000?
3. What is the probability that the debt for a borrower with good credit is between $12,000 and $18,000?
4. What is the probability that the debt for a borrower with good credit is no more than $14,000?