# QNT351 QNT/351 Week 4 Problems - 22987

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1. Determine whether the random variable is discrete or continuous.

a. the number of textbook authors now sitting at a computer

b. the weight of a T-bone steak

c. the number of fish caught during a fishing tournament

d. the time it takes to fly from city A to city B

e. the number of points scored during a basketball game

2. Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

(a) the number of light bulbs that burn out in the next week in room with 17 bulbs

(b) the amount of rain in City B during April

The random variable x has the following discrete probability distribution. Complete parts a trough f.

4. A discrete random variable x can assume five possible values 2, 3, 5, 7, and 9. Its probability distribution is shown here. Complete parts a trough c.

5. Toss three fair coins and let x equal the number of tails observed.

a. Identify the sample points associated with this experiment and assign a value of x to each sample point

b. Calculate p(x) for the values x=1 and x=2

c. Construct a graph for p(x)

d. What is P(x=2 or x=3)?

6. Find the following probabilities for the standard normal random variable z.

a. P(z>1.79)  b. P(z< -1.46)  c. P(0.54 ≤ z ≤ 2.67)  d. P(- 2.34 < z > 1.77)

7. Find the area under the standard normal probability distribution between the following pairs of z – scores.

a. z=0 and z=3.00

b. z=0 and z=1.00

c. z=0 and z=2.00

d. z=0 and z=0.62

8. Find the area under the standard normal probability distribution between the following pairs of z – scores.

a. z=0 and z=1.00

b. z=0 and z=2.00

c. z=0 and z=3.00

d. z=0 and z=0.62

9. Find the following probability for the standard normal random variable z.

P( - 1.5 ≤ z ≤ 1.5)

10. Suppose the random variable x is best described by a normal distribution with µ = 26 and ? = 5. Find the z score that corresponds to each of the following x – values.

a. x=17  b. x=26  c. x=11  d. x=13   e. x=20   f. x=32

11. Suppose x is a normal distributed random variable with µ = 11 and ? = 2. Find each of the following probabilities.

a. P(x≥14.5)   b. P(x≤9)   c. P(12.56≤x≤16.12)   d. P(5.84≤x≤13.42)

12. The ages of a group of 50 women are approximately normally distributed with a mean of 48 years and a standard deviation of 5 years. One woman is randomly selected from the group, and her age is observed.

a. Find the probability that her age will fall between 55 and 59 years.

b. Find the probability that her age will fall between 47 and 53 years.

c. Find the probability that her age will be less than 35 years.

d. Find the probability that her age will exceed 41 years

13. Financial analysts who make forecasts of stock prices are categorized as either “buy-side” analysts or “sell-side” analysts. The mean and standard deviation of the forecast errors for both types of analysts are shown is the table to the right. Assume that the distribution of forecast errors are approximately normally distributed.

a. Find the probability that a buy-side analyst has a forecast error of + 2.01 or higher (mean 0.85, standard deviation 1.96)

b. Find the probability that a sell-side analyst has a forecast error of + 2.01 or higher (mean -0.05, standard deviation 0.83)

14. The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.5 miles per gallon.

a. What is the probability that a randomly selected hybrid gets more than 62 miles per gallon?

b. What is the probability that a randomly selected hybrid gets 50 miles per gallon or less?

c. What is the probability that a randomly selected hybrid gets between 57 and 62 miles per gallon?

d. What is the probability that a randomly selected hybrid gets less than 46 miles per gallon?

15. Resource Reservation Protocol (RSVP) was originally designed to establish signaling links for stationary networks. RSVP was applied to mobile wireless technology. A simulation study revealed that the transmission delay (measured is milliseconds) of an RSVP linked wireless device has an approximate normal distribution with mean µ=46.5 milliseconds and ? = 8.5 milliseconds. Complete part a and b.

a. What is the probability that the transmission delay is less than 57 milliseconds?

b. What is the probability that the transmission delay is between 40 and 60 milliseconds?

Solution Description

1. Determine whether the random variable is discrete or continuous.

a. the number of textbook authors now sitting at a computer

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