a) A company produces a range of snack foods, including cookies. The cookies are produced so...
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a) A company produces a range of snack foods, including cookies. The cookies are produced so that the weight of each cookie is normally distributed with a mean of 27g and a standard deviation of 0.6g. The cookies are then packaged in groups of 8, with an advertised net weight of 210g. Note: You may use Excel functions to answer the following questions however in order to gain full marks for a. parts ii, iii, iv and v and also b. part ii you must provide logical working that includes the Excel function, the Excel output and an appropriate diagram. i) If X is the random variable representing the weight of a single cookie, then identify the type of distribution the random variable X has and write down the value(s) of the parameter(s) of this distribution. (2 marks) ii) Determine the probability that a randomly selected cookie has a weight of less than 25.5g. (4 marks) iii) Calculate the proportion of cookies produced with weight greater than 28g. (4 marks) iv) Calculate the proportion of cookies produced that have a weight within 0.7g of the population mean. v) Find the weight that 97.5% of cookies will exceed. (5 marks) (3 marks) b) The quality control officer for the company is looking at the likelihood of packs of cookies being under the advertised weight. His interest therefore shifts to the mean weight of cookies in a sample of 8, which will be denoted X i) State the distribution of the mean of a sample of 8 randomly selected cookies (that is, X) and give the value(s) of its parameter(s). ii) (3 marks) Determine the mean weight of cookies in a pack in order for the total contents to be 210g. Hence determine the probability that a randomly selected pack of cookies has a weight that is below the advertised weight. (4 marks) a) A company produces a range of snack foods, including cookies. The cookies are produced so that the weight of each cookie is normally distributed with a mean of 27g and a standard deviation of 0.6g. The cookies are then packaged in groups of 8, with an advertised net weight of 210g. Note: You may use Excel functions to answer the following questions however in order to gain full marks for a. parts ii, iii, iv and v and also b. part ii you must provide logical working that includes the Excel function, the Excel output and an appropriate diagram. i) If X is the random variable representing the weight of a single cookie, then identify the type of distribution the random variable X has and write down the value(s) of the parameter(s) of this distribution. (2 marks) ii) Determine the probability that a randomly selected cookie has a weight of less than 25.5g. (4 marks) iii) Calculate the proportion of cookies produced with weight greater than 28g. (4 marks) iv) Calculate the proportion of cookies produced that have a weight within 0.7g of the population mean. v) Find the weight that 97.5% of cookies will exceed. (5 marks) (3 marks) b) The quality control officer for the company is looking at the likelihood of packs of cookies being under the advertised weight. His interest therefore shifts to the mean weight of cookies in a sample of 8, which will be denoted X i) State the distribution of the mean of a sample of 8 randomly selected cookies (that is, X) and give the value(s) of its parameter(s). ii) (3 marks) Determine the mean weight of cookies in a pack in order for the total contents to be 210g. Hence determine the probability that a randomly selected pack of cookies has a weight that is below the advertised weight. (4 marks)
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