Find the standard deviation for the given probability distribution. \[\begin{array} { c | c } \mathrm { x } & \mathrm { P } ( \mathrm { x } ) \\ \hline 0 & 0.27 \\ \hline 1 & 0.07 \\ \hline 2 & 0.07 \\ \hline 3 & 0.22 \\ \hline 4 & 0.37 \end{array}\]

A) 2.87 B) 1.28 C) 1.73 D) 2.73 E) 1.65 A) 2.87 B) 1.28 C) 1.73 D) 2.73 E) 1.65

In the 4 × 100 relay event,each of four runners runs 100 metres.A university team is preparing for a competition.The means and standard deviations of the times (in seconds)of their four runners are as shown in the table: \[\begin{array} { c | c | c } \text { Runner } & \text { Mean } & \text { SD } \\ \hline 1 & 12.19 & 0.12 \\ 2 & 12.37 & 0.14 \\ 3 & 12.01 & 0.08 \\ 4 & 11.73 & 0.07 \end{array}\] What are the mean and standard deviation of the relay team's total time in this event? Assume that the runners' performances are independent.

A) ? = 48.3 sec,? = 12.64 sec B) ? = 48.3 sec,? = 0.045 sec C) ? = 24.15 sec,? = 0.21 sec D) ? = 48.3 sec,? = 0.21 sec E) ? = 24.15 sec,? = 12.64 sec A) ? = 48.3 sec,? = 12.64 sec B) ? = 48.3 sec,? = 0.045 sec C) ? = 24.15 sec,? = 0.21 sec D) ? = 48.3 sec,? = 0.21 sec E) ? = 24.15 sec,? = 12.64 sec

Jo is a hairstylist.The probability model below describes the number of clients that she may see in a day. \[\begin{array} { l | c c c c c c } \text { Number of clients } & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Probability } & 0.05 & 0.15 & 0.15 & 0.3 & 0.2 & 0.15 \end{array}\] What is the standard deviation of the number of clients that Jo sees per day?

A) 1.31 B) 1.41 C) 2.19 D) 1.99 E) 1.55 A) 1.31 B) 1.41 C) 2.19 D) 1.99 E) 1.55

Exam 14: Random Variables

On one tropical island,hurricanes occur with a mean of 2.37 per year.Assuming that the number of hurricanes can be modeled by a Poisson distribution,find the probability that during the next 2 years the number of hurricanes will be 3.

(Multiple Choice)

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Question 181

An insurance company estimates that it should make an annual profit of $150 on each homeowner's policy written,with a standard deviation of $6000.If it writes three of these policies,the mean annual profit for the company is found to be $3 \times 150 = 450$ The standard deviation of the company's annual profit is found to be $\sqrt { 6000 ^ { 2 } + 6000 ^ { 2 } + 6000 ^ { 2 } } \approx \$ 10,392 .$ The calculation of the standard deviation requires the assumption that the policies are independent of one another.Which of the following examples describes a situation in which that assumption may be violated? A: The houses are close to each other and may all be affected by the same catastrophe such as earthquake,flooding,or fire. B: The owners all bought their homes in the same year and may all be affected by a downturn in the market. C: The owners of the three homes are related. D: All three houses were bought for the same price.

(Multiple Choice)

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Question 182

Find the standard deviation for the given probability distribution. () 0 0.27 1 0.07 2 0.07 3 0.22 4 0.37

(Multiple Choice)

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Question 183

You have arranged to go camping for two days in March.You believe that the probability that it will rain on the first day is 0.4.If it rains on the first day,the probability that it also rains on the second day is 0.5.If it doesn't rain on the first day,the probability that it rains on the second day is 0.3.Let the random variable X be the number of rainy days during your camping trip.Find the standard deviation of X.

(Multiple Choice)

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Question 184

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 4X + 19.Round to two decimal places if necessary. Mean SD 100 14 120 7

(Multiple Choice)

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Question 185

A tennis player makes a successful first serve 70% of the time.If she serves 80 times,is it appropriate to use a Normal model to approximate the distribution of the number of good first serves? Assume that each serve is independent of the others.

(Multiple Choice)

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Question 186

A carnival game offers a $120 cash prize for anyone who can break a balloon by throwing a dart at it.It costs $9 to play and you're willing to spend up to $36 trying to win.You estimate that you have a 10% chance of hitting the balloon on any throw.Find the expected amount you will win.Assume that throws are independent of each other.

(Multiple Choice)

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Question 187

Suppose the probability of contracting a certain disease is p = 0.0004 for a new case in a given year.What is the expected number of new cases in a year in a town where 4000 people do not currently have the disease?

(Multiple Choice)

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Question 188

In the 4 × 100 relay event,each of four runners runs 100 metres.A university team is preparing for a competition.The means and standard deviations of the times (in seconds)of their four runners are as shown in the table: Runner Mean SD 1 12.19 0.12 2 12.37 0.14 3 12.01 0.08 4 11.73 0.07 What are the mean and standard deviation of the relay team's total time in this event? Assume that the runners' performances are independent.

(Multiple Choice)

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Question 189

A tennis player usually makes a successful first serve 69% of the time.She buys a new racket hoping that it will improve her success rate.When she first tests her new racket she makes 4 first serves in a row.Is this evidence that with the new racket her success rate has improved? In other words,is a streak like this unusual for her? Explain.

(Multiple Choice)

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Question 190

A carnival game offers a $80 cash prize for anyone who can break a balloon by throwing a dart at it.It costs $5 to play and you're willing to spend up to $20 trying to win.You estimate that you have a 8% chance of hitting the balloon on any throw.Find the standard deviation of the number of darts you throw.Assume that throws are independent of each other.

(Multiple Choice)

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Question 191

A tennis player makes a successful first serve 54% of the time.If she serves 5 times,what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

(Multiple Choice)

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Question 192

Jo is a hairstylist.The probability model below describes the number of clients that she may see in a day. Number of clients 0 1 2 3 4 5 Probability 0.05 0.15 0.15 0.3 0.2 0.15 What is the standard deviation of the number of clients that Jo sees per day?

(Multiple Choice)

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Question 193

A hair salon claims that 90% of their customers are satisfied.However,Toni who recently started working there found that of 120 customers last week,only 100 were satisfied.If it were true that on average 90% of customers are satisfied,what is the chance that among 120 customers 100 or fewer would be satisfied?

(Multiple Choice)

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Question 194

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 0.3Y. Mean SD 70 7 60 8

(Multiple Choice)

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Question 195

The probability that a call received by a certain switchboard will be a wrong number is 0.02.Use the Poisson approximation to the binomial distribution to find the probability that among 140 calls received by the switchboard,there are no wrong numbers.

(Multiple Choice)

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Question 196

Police estimate that in one city 48% of drivers wear their seat belts.They set up a safety roadblock,stopping cars to check for seat belt use.If they stop 70 cars during the first hour,what is the mean number of drivers expected to be wearing their seat belts?

(Multiple Choice)

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Question 197

In a box of 7 batteries,3 are dead.You choose two batteries at random from the box.Let the random variable X be the number of good batteries you get.Find the probability model for X.

(Multiple Choice)

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Question 198

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 3X - Y.Round to two decimal places if necessary. Mean SD 190 15 170 19

(Multiple Choice)

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Question 199

A laboratory worker finds that 1.8% of his blood samples test positive for the HIV virus.If 270 blood samples are selected at random,is it appropriate to use a Normal model to approximate the distribution of the number that test positive for the HIV virus?

(Multiple Choice)

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Question 200

Showing 181 - 200 of 215

Exam 14: Random Variables

On one tropical island,hurricanes occur with a mean of 2.37 per year.Assuming that the number of hurricanes can be modeled by a Poisson distribution,find the probability that during the next 2 years the number of hurricanes will be 3.

Find the standard deviation for the given probability distribution. () 0 0.27 1 0.07 2 0.07 3 0.22 4 0.37

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 4X + 19.Round to two decimal places if necessary. Mean SD 100 14 120 7

A tennis player makes a successful first serve 70% of the time.If she serves 80 times,is it appropriate to use a Normal model to approximate the distribution of the number of good first serves? Assume that each serve is independent of the others.

Suppose the probability of contracting a certain disease is p = 0.0004 for a new case in a given year.What is the expected number of new cases in a year in a town where 4000 people do not currently have the disease?

A tennis player makes a successful first serve 54% of the time.If she serves 5 times,what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

Jo is a hairstylist.The probability model below describes the number of clients that she may see in a day. Number of clients 0 1 2 3 4 5 Probability 0.05 0.15 0.15 0.3 0.2 0.15 What is the standard deviation of the number of clients that Jo sees per day?

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 0.3Y. Mean SD 70 7 60 8

The probability that a call received by a certain switchboard will be a wrong number is 0.02.Use the Poisson approximation to the binomial distribution to find the probability that among 140 calls received by the switchboard,there are no wrong numbers.

Police estimate that in one city 48% of drivers wear their seat belts.They set up a safety roadblock,stopping cars to check for seat belt use.If they stop 70 cars during the first hour,what is the mean number of drivers expected to be wearing their seat belts?

In a box of 7 batteries,3 are dead.You choose two batteries at random from the box.Let the random variable X be the number of good batteries you get.Find the probability model for X.

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 3X - Y.Round to two decimal places if necessary. Mean SD 190 15 170 19

A laboratory worker finds that 1.8% of his blood samples test positive for the HIV virus.If 270 blood samples are selected at random,is it appropriate to use a Normal model to approximate the distribution of the number that test positive for the HIV virus?

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