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Question : Find (by inspection) the expected value and standard deviation of the random variable with the : 2163583

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

21) Find (by inspection) the expected value and standard deviation of the random variable with the following density function: f(x) = (7/√(2π))e^{-49/2(x - 3.9)^2}

Enter your answer as just two numbers (a real number to one decimal place followed by a reduced fraction) separated by a comma, the first representing E(X) and the second representing √(Var(X)).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

22) A random variable X is exponentially distributed with a mean of 2. Find Pr(1 ≤ X ≤ 3).

A) (1/2)e^{-3/2}

B) e^{-1/2} - e^{-3/2}

C) (1/2)(e^{-1} - e^{-3})

D) (1/2)e^{-1/2}

E) none of these

23) A random variable X is exponentially distributed with a mean of 10. Determine a so that Pr(0 ≤ x ≤ a) = 0.75.

A) a = (1/10)ln4

B) a = ln0.75

C) a = (1/10)

D) a = ln(3/4)

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

24) A survey shows that the time spent in a checkout line in a certain supermarket has an exponential density function with mean 5 minutes. What is the probability of spending 10 minutes or more in a checkout line? Enter just a real number rounded off to two decimal places.

25) It is estimated that the time between arrivals of visitors to a public library is an exponential random variable with expected value of 13 minutes. Find the probability that 30 minutes elapses without any arrivals. Enter your answer as just e^{a/b}, where (a/b) is a reduced fraction.

26) An appliance comes with an unconditional money back guarantee for its first 6 months. It has been found that the time before the appliance experiences some sort of malfunction is an exponential random variable with mean 2 years. What percentage of appliances will malfunction during the warranty period? Enter your answer as just a ± e^{b}, where a is an integer and b is a real number to two decimal places. (no units).

27) When a road crew inspects a road that hasn't been worked on for several years, then the distance between necessary repairs is an exponential random variable with a mean of 0.25 miles. What is the probability that the crew will find a mile long stretch of road that does not need repairs? Enter your answer as just e^{b}.

28) Let X be the time to failure of an electronic component, and suppose X is an exponential random variable with E(X) = 4 years. Find the median lifetime, i.e., find M such that Pr(X ≤ M) = (1/2). Enter just a real number rounded to two decimal places (no units).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

29) The number of new mini-vans sold by a particular salesperson during the month of March is exponentially distributed with a mean of 8. What is the probability that the salesperson will sell between 4 and 8 mini-vans in March?

A) 0.184

B) 0.233

C) 0.239

D) 0.172

Determine the area under the standard normal curve that lies between:

30) z = 1 and z = 2

A) 0.8641

B) 0.0008

C) 0.1359

D) 0.0006

31) z = 0.9 and z = 1.4

A) 0.1841

B) 0.9192

C) 0.8159

D) 0.1033

32) z = -0.7 and z = 0.7

A) 0.516

B) 0.758

C) 0.242

D) 0.5

33) z = -2 and z = -0.9

A) 0.1841

B) 0.0228

C) 0.8159

D) 0.1613

34) A table saw cuts construction studding. Observation has shown that the lengths of the studs are normally distributed with a mean of 10 feet and a standard deviation of 6 inches. Which of the following correctly represents the probability that a randomly chosen stud exceeds 11 feet?

A)

B)

C)

D)

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

35) A lumber yard cuts 2" x 4" lumber into 8 foot studs. It is observed that the actual lengths of the studs are normally distributed with mean 8 feet and standard deviation 1 foot. What proportion of the studs are longer than 8.25 feet? Enter just a real number rounded off to two decimal places.

36) A farmer has observed that the time to maturation of a certain crop is approximately normally distributed with a mean of 60 days and a standard deviation of 2 days. Find the percentage of plants that will mature in less than 55 days. Enter the percentage as just a real number rounded off to two decimal places followed by %.

37) When mice are placed in a certain maze the amount of time it takes them to go through the maze is approximately normally distributed with a mean of 25 minutes and a standard deviation of 5 minutes. What is the probability that a mouse will complete the maze in under 30 minutes? (Hint: find the normal density function first). Enter just a real number rounded off to two decimal places.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

38) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 332 seconds.

A) 0.0107

B) 0.5107

C) 0.4893

D) 0.9893

39) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 345 seconds to run the mile.

A) 0.9893

B) 0.0107

C) 0.5107

D) 0.4893

40) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.24 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains fewer than 12.14 ounces of beer.

A) 0.5062

B) 0.4938

C) 0.9938

D) 0.0062