What is the approximate distribution of the sample mean weight of the random sample of 36 ripe tomatoes

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Activity 1

(i)       The intervals between successive events in a Poisson process are exponentially distributed.  Using Minitab, find the mean and standard deviation of the intervals between earthquakes in California.  Are these values consistent with the data being observations from an exponential distribution?  Give a reason for

your answer.       

(i)       Calculate the value of the upper quartile for this distribution.                    [3]

(ii)   On a copy of, or very rough sketch based on, Figure 1, show the

values of α and its corresponding quantile qα  for the upper quartile that you calculated in part (c)(i).                                                                                                                                                                     Activity 2:

B) The Minitab file body-temperature.mwx contains values of the normal body temperature, measured orally, of n = 130 people.  The model for normal human body temperature used in part (a) of this question was obtained partly by consideration of these data.  The data can be used to check whether or not it is appropriate to assume that normal human body temperature can be modelled by a normal distribution.

Suggest a suitable graph to investigate specifically whether or not a normal distribution might be a good model for the normal body temperature of people, measured orally.  Using the Mean Rank (Herd-Johnson) method in Minitab (see Activity 7 of Computer Book B), produce this graph.  Include a copy of your graph in your answer.  On the basis of this graph, do you think that a normal distribution is a plausible model for these data?  Explain your answer.              [5]

(C)   Suppose that the mean weight of a particular type of ripe tomato is 155 g, and the variance of the weight of this type of ripe tomato is 576 g2.  A random sample of n = 36 such ripe tomatoes is obtained.

(i)     What is the approximate distribution of the sample mean weight of the random sample of 36 ripe tomatoes?                                                         [2]

(ii)   Use Minitab to find the probability that the sample mean weight of the sample of 36 ripe tomatoes lies between 150 g and 157.5 g.  To show that you used Minitab, write down the results of any intermediate calculations that you make in Minitab to the same number of decimal places as given by Minitab.                                              

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