Statistics and Probability Answers

The aluminum bottle, first introduced in 1991 by CCL Container for mainly personal and household items such as lotions, has become popular with beverage manufacturers. Besides being lightweight and requiring less packaging, the aluminum bottle is reported to cool faster and stay cold longer than typical glass bottles. A small brewery tests this claim and obtains the following information regarding the time (in minutes) required to chill a bottle of beer from room temperature (75ºF) to serving temperature (45ºF). At α = 0.10, can it be concluded that aluminum bottles chills at a lesser time than glass bottles?

Aluminum Glass

Sample Size 35 42

Mean time to chill 92.4 133.8

Sample standard deviation 7.3 9.9

a. State the hypothesis and identify the claim of the researcher.

b. Find the critical value(s).

c. Compute the test value.

d. Make a decision on the null hypothesis.

e. Make a decision on the claim of the researcher.

a population consists of three numbers (2,5,9). Consider all possible samples of size 2 which can be drawn from the population. Find the variance of the sampling distribution of the sample means.

1.     The time for a major exam to be completed is normally distributed with an average of 55 minutes and a standard deviation of 9 minutes. If 92% of the students completed the exam, when should the test be terminated?

A chef at a restaurant feels that the amount of time that people spend waiting in line to get served is too long. To determine if a new loading and unloading procedure effectively reduces the wait time, he measures the amount of time (in minutes) people are waiting in line for seven days. To make a reasonable comparison, he chooses times when weather conditions are similar.

                                     Mon         Tues        Wed         Thurs        Fri            Sat           Sun

                                    2p.m         2p.m        2p.m        2p.m        2p.m        2p.m        2p.m

Wait time before X1      12            26            20             38            57            82             57

Wait time after X2        11            28            19             36            59            75             55

Is the new loading and unloading procedure effective in reducing the wait time at the a=0.05 level of significance?

1. State the null hypothesis and identify the claim.
2. Find the critical value
3. Test Value
4. Make a decision on the hypothesis
5. Make a decision on the claim.

The record of births, over the last 100 years maintained by the municipal council of a town showed that 200 children were born blind during that period. On the assumption that the number of children born blind in an year follows Poisson distribution, estimate the number of years in which there were (a) no blind births (b) one blind birth (c) two blind births 

the average time it takes for a college student to complete a certain examination is 46.2 minutes.the standard deviation is 8 minutes.assume the variable is normally distributed. find the probability that a randomly selected college student will complete the examination in less than 43 minutes

1.  On a recent math test, the mean score was 75 and the standard deviation was 5. Mike scored an 85.

a)     What percent of the students scored below Mike?

b)    What percent of the students scored above Mike?

c)     If the class had 150 students in it, how many of them would you expect to score higher than Mike?

d)    If the class had 220 students in it, how many of them would you expect to score lower than Mike? 

A man takes either a Metrobus or Metrorail to work, with probabilities 0.4 and 0.6 respectively. When he 

takes the bus, he is late on 25% of the days. When he takes the train, he is late on 15% of the days. If the 

man is late for work on a particular day, what is the probability he took the bus?

A courier company has two vehicles available for local deliveries. Because of the demand on their time and 

the chance of mechanical failure, the probability that a specific vehicle will be available when needed is 

0.85. The availability of one vehicle is independent of the other.

4.1 In the event of large orders, what is the probability that both vehicles will be available?

4.2 What is the probability that none of the vehicles will be available?