Microsoft Word - Assignment _120_2021.doc 1 INU0120 – Statistics Assignment Student Number This assignment requires you to apply your understanding of recent topics involving probability, normal...

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Microsoft Word - Assignment _120_2021.doc 1 INU0120 – Statistics Assignment Student Number This assignment requires you to apply your understanding of recent topics involving probability, normal distribution and sampling distribution to the following situation. The maximum mark available for each part is shown in brackets. Answer all parts. In each case make sure to show all your working. Failure to show all necessary working will lose credit. The number of marks available for each part is shown in brackets. Total marks = 30. -------------------------------------------------------------------------------------------------------------------------- A pharmaceutical company manufactures tubes of a certain skin cream. The tubes have a stated volume of 250 ml, where the volume has a normal distribution with a mean, µ and a standard deviation, 0.6 ml. If the company requires no more than 1% of all tubes sold to contain less than the stated volume, a) State the normal distribution and sketch neatly a normal distribution curve to illustrate the situation of meeting the company’s requirement. (5) b) Calculate the minimum value for the mean so that the company’s requirement is met, giving your answer to the nearest 0.1 ml. (4) Since, the mean of the volume in the tubes can drift over time, the company undertakes regular checks on the production process to ensure that the company’s requirement continues to be met. As part of a regular monitoring of the production process, the company selects a sample of 15 tubes randomly from the production line. If the observed mean of the sample is 251.8 ml, c) State the sampling distribution and determine the standard error of the mean. (4) d) Determine a 99% confidence interval for the mean volume of the distribution, giving the limits for the interval to the nearest 0.1 ml. (5) e) Based on the observed sample, explain why the company can be actually 99.5% confident its requirement is being met. (3) f) Hence, explain by what percentage the company’s requirement is not met. (1) g) If the actual mean µ is 251.8 ml, determine the percentage of tubes containing less than 250 ml. (3) For the future, the company decides that a 95% confidence interval will be adequate, but that it should be no more than 0.5 ml wide. h) Determine the minimum sample size required to achieve such a confidence interval for the mean. (5) Munir Obeidat 2 Do not write in margin 3 Do not write in margin 4 Do not write in margin 5 Do not write in margin