Elementary Statistics Math Problems

1.Letzbe a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(1.11z2.72) =

2. Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.) The area between z=2.26 andz=1.42is

3. Most exhibition shows open in the morning and close in the late evening. A study of Saturday arrival times showed that the average arrival time was 3 hours and 48 minutes after the doors opened, and the standard deviation was estimated at about55minutes. Assume that the arrival times follow a normal distribution.

(a) At what time after the doors open will88%of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.) minutes after doors open (b) At what time after the doors open will only12%of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.) minutes after doors open (c) Do you think the probability distribution of arrival times for Friday might be different from the distribution of arrival times for Saturday? Explain your answer.

4. A person's blood glucose level and diabetes are closely related. Letxbe a random variable measured in milligrams of glucose per deciliter(1/10 of a liter)of blood. Suppose that after a12-hourfast, the random variablexwill have a distribution that is approximately normal with mean=80and standard deviation=26.Note:After 50 years of age, both the mean and standard deviation tend to increase. For an adult(under 50)after a12-hourfast, find the following probabilities. (Round your answers to four decimal places.)

(a)xis more than 60 (b)xis less than 110 (c)xis between 60 and 110 (d)xis greater than 125 (borderline diabetes starts at 125)

5. Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of6.8minutes and a standard deviation of1.9minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between3and8minutes (b) the response time is less than3minutes (c) the response time is more than8minutes

6. Supposexhas a distribution with=52and=8. FindP(48x53). (Round your answer to four decimal places.)

7. Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 82 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean = 82 tons and standard deviation = 1.3 ton.

What is the probability that 22 cars chosen at random will have a mean load weight x of less than 81.5 tons of coal? (Round your answer to four decimal places.)

8. Suppose x has a distribution with a mean of 60 and a standard deviation of 45. Random samples of size

n = 36 are drawn.

(b) Find the z value corresponding to

x = 67.5. z =

(c) Find P(x < 67.5). (Round your answer to four decimal places.) P(x < 67.5) =

9. Supposexhas a distribution with=25and=24.

(a) If a random sample of sizen=33is drawn, find_x,_xandP(25x27). (Round_xto two decimal places and the probability to four decimal places.)

_x=

_x=

P(25x27) =

(b) If a random sample of sizen=73is drawn, find_x,_xandP(25x27). (Round_xto two decimal places and the probability to four decimal places.)

_x=

_x=

P(25x27) =