TMA 03 See module website for the cut-off date. Question 1, which covers topics in Unit 5, and Question 2, which covers topics in Unit 6, form M248 TMA 03. Question 1 is marked out of 28; Question 2 is marked out of 22. Question 1 28 marks You should be able to answer this question after working through Unit 5. (a) In this part of the question, you should calculate the required probabilities without using Minitab, and show your working. (You may use Minitab to check your answers, if you wish.) In England, the most serious emergency calls requesting an ambulance are classified as Red 1 . According to data from NHS England, in March 2017, the London Ambulance Service (LAS) received a total of 1597 Red 1 emergency calls. Based on this number and adjusting for variations during the day, suppose that Red 1 calls arriving at the LAS in daylight hours may be modelled as a Poisson process with rate 3 per hour. (i) (1) Write down the distribution of the number of Red 1 calls arriving at the LAS in a 30-minute period during daylight hours, including the values of any parameters. [2] (2) Calculate and report the probability that three Red 1 calls arrive at the LAS in 30 minutes during daylight hours. [2] (ii) (1) Write down the distribution of the waiting time (in hours) between the arrivals of two successive Red 1 calls at the LAS during daylight hours, including the values of any parameters. [2] (2) Calculate and report the probability that the gap between the arrivals of two successive Red 1 calls at the LAS during daylight hours will exceed 20 minutes. [4] (b) This part of the question concerns data on the lengths of the 51 time intervals (in days) between successive earthquakes in California, starting from a major earthquake on 9 January 1857, up to an earthquake on 24 August 2014. (To qualify for inclusion in this dataset, earthquakes had to be single mainshocks with magnitude at least 4.9.) These time intervals are in the variable Interval in the worksheet california-earthquakes.mwx. In this part of the question, you will explore whether or not a Poisson process is a suitable model for these data. (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. [3] (ii) Using Minitab, obtain a histogram with the following properties: the ticks on the horizontal axis are at the cutpoints the bins have width 500 days the first bin starts at 0 days and the last bin finishes at 7500 days. Include a copy of your histogram in your answer. Is the shape of the histogram consistent with the data being observations from an exponential distribution? Give a reason for your answer. [4] (iii) The data are listed in the order in which they arose. Using Minitab, produce an appropriate graph to investigate whether, for the period of observation, the data are consistent with the rate at which earthquakes occur in California remaining constant. Include a copy of your graph in your answer. Explain why your graph suggests that the average rate at which earthquakes occurred in California was not constant over the period. How did the average rate change over time? [6] (c) A certain form of triangular distribution has c.d.f. F (x) = 1 (1 x)2, 0 < x < 1, which is plotted in Figure 1. (It is called a triangular distribution because its p.d.f. is a line which, together with the axes, forms a triangle.) F(x) 1 0 0 1 x Figure 1 The c.d.f. F (x) (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 and its corresponding quantile q for the upper quartile that you calculated in part (c)(i). [2] Question 2 22 marks You should be able to answer this question after working through Unit 6. (a) In this part of the question, you should calculate the required probabilities using tables, not Minitab, and show your working. (You may use Minitab to check your answers, if you wish.) A model for normal human body temperature, X, when measured orally in F, is that it is normally distributed, X N(98.2, 0.5184). (i) According to the model, what proportion of people have a normal body temperature of 99 F or more? [3] (ii) Find the normal body temperature such that, according to the model, only 10% of people have a lower normal body temperature. [2] 9 (iii) Let W denote normal human body temperature, when measured orally in C. Given that W = 5 (X 32) and X N(98.2, 0.5184), what is the distribution of W ? [3] (iv) According to the model that you just derived for W , what proportion of people have a normal body temperature of between 36 C and 36.8 C? [4] (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. [3]

**WE OFFER THE BEST CUSTOM PAPER WRITING SERVICES. WE HAVE DONE THIS QUESTION BEFORE, WE CAN ALSO DO IT FOR YOU.**- Assignment status: Already Solved By Our Experts
*(USA, AUS, UK & CA PhD. Writers)***CLICK HERE TO GET A PROFESSIONAL WRITER TO WORK ON THIS PAPER AND OTHER SIMILAR PAPERS, GET A NON PLAGIARIZED PAPER FROM OUR EXPERTS**

- 24/7 Customer Support
- All Subject Areas
- Money-Back Guarantee
- Timely Delivery
- Originality report
- Confidentiality guaranteed

You can get our ideal online homework help services with four easy steps. All you have to do is inform us of your requirements. Immediately we will match with a specialist in your academic discipline. After that, we will track your order, review it to ensure it meets your requirements, and submit it to your email.

Fill in your assignment instructions on the order form

Immediately you contact us for homework help; we will assign your assignment to an academic expert.

We have a team of editors, who will thoroughly review your assignment, ensuring there are no errors before submission

Once we have completed the assignment, we will deliver it to your account. Additionally, we will send a notification to your email.

Once you consult us for homework help online services, you will attest to why we are among the USA's best essay writing services.

Read on and find out some of the features that make our services superlative.

You can confirm that the content you get is original for free using our plagiarism checker.

We offer unlimited access to our essay homework samples.

Once you place an order, we format it accordingly without demanding additional charges.

We offer free unlimited revisions until your assignment is of your desired quality..

We have a team of specialized editors who review your assignment before submission.

You can track the progress of your homework for free.