Question;QNT;351 Week 4 Problems;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;3. The random variable x has the following;discrete probability distribution. Complete parts a trough f.;a.;List the values x may assume.;b.;What value of x is most probable?;c.;Display the probability distribution as a graph. Choose the correct graph bellow.;d.;Find P(x=8);e.;Find P(x?5);f.;Find P(x>2);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.;a.;What is p(5)?;b.;What is the probability that x equals 2 or 9?;c.;What is p (x?7)?;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 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 ? = 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 ? = 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;b.;Find the probability that a sell-side analyst has a forecast error of + 2.01 or;higher;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 ?=46.5;milliseconds and? = 8.5 milliseconds.;Complete;part a and b.
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