Statistics and Probability Answers

The factory owner claimed that their bottled fruit juice has the capacity of less than an average of 280ml. To test the claim, a group of consumers gets a sample of 80 bottles of the fruit juice, calculates the capacity, and then finds the mean capacity to be 265ml. The standard deviation is 8ml. Use a= 0.05 level of significance to test the claim.

Suppose that the lifetimes of electric light bulbs follow an Exponential distribution with mean

1000 hours. A

random sample of 40 light bulbs is tested. The probability that the mean

lifetime is at least 900 hours is:

A store contains 1 pair of boots with each of the following colors are black, chocolate and yellow. Each pair is put together in a particular place. You enter into the dark store and pick randomly the boot without looking at it. Then, you replace it with another boots. What is the probability that you will choose the black pair of boots both times?

5. A coin is tossed 400 times. Use the normal curve approximation to find the probability of obtaining

(a) between 185 and 210 heads inclusive;

(b) exactly 205 heads;

(c) fewer than 176 or more than 227 heads

4. The heights of 1000 students are normally distributed with a mean of 175 centimeters and a standard deviation of 7 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would you expect to have heights

(a) less than 160.0 centimeters?

(b) between 171.5 and 182.0 centimeters inclusive?

(c) equal to 175.0 centimeters?

(d) greater than or equal to 188.0 centimeters?

The lengths (in minutes) of a random selection of popular children’s animated films are

listed below. Estimate the true mean length of all children’s animated films with 95%

confidence.

90 84 83 91 75 88 78 96 78 79 77

2. Changes in airport procedures require considerable planning. Arrival rates of aircraft are important factors that must be taken into account. Suppose small aircraft arrive at a certain airport, according to a Poisson process, at the rate of 5 per hour. Thus, the Poisson parameter for arrivals over a period of hours is μ = 5t.

(a) What is the probability that exactly 4 small aircraft arrive during a 1-hour period?

(b) What is the probability that at least 4 arrive during a 1-hour period?

(c) If we define a working day as 12 hours, what is the probability that at least 75 small aircraft arrive during a working day?

Activity 1: Draw Me

Directions: Given the following information, construct the rejection region. Show the solution in a step-by-step procedure.

1. H0 : = 84

Ha : 84

m= 87, s= 10, n = 35, alpha= 0.05

2. H0 : = 45

Ha : < 45

m= 40, s = 12, n = 32, alpha= 0.01

The average zone of inhibition (in mm) for mouthwash L as tested by the medical technology students has been known to be 9mm. A random sample of 10 mouthwash L was tested and the test yielded an average zone of inhibition of 7.5mm with a variance of 25 mm. Is there enough reason to believe that the anti-bacterial property of the mouthwash has decreased? Test the hypothesis that the average zone of inhibition of the mouthwash is no less than 9mm using 0.05 level of significance.

A. State the hypotheses.

B. Determine the test statistic to use.

C. Determine the level of significance, critical value, and the decision rule.

D. Compute the value of the test statistic.

E. Make a decision.

F. Draw a conclusion.

If the average time spent studying is 10 hours and the standard deviation is 4 hours, what it the probability that a student will spend more than 13 hours studying?