SECTION B: NORMAL DISTRIBUTION Question B1 [4 marks] The number of minutes per week that students spend surfing the internet is normally distributed with a mean of 490 minutes and standard deviation of 45 minutes. Calculate the probability that the time, in a week, a student spends surfing the internet is: 1) less than 440 minutes 2) more than 525 minutes. 3) between 405 minutes and 565 minutes. 4) at least an hour every day on average. Question B2 [3 marks] A vending machine dispenses coffee into cups. The amount of coffee dispensed has a mean of 127 ml with a standard deviation of 9.6 ml. Assume that the amount of coffee dispensed is normally distributed. 1) The cup has a volume of 150ml. Calculate the probability that a cup will overflow when coffee is dispensed. to 4 dp to 4 dp. to 4 dp to 4 dp to 4 dp 2) A sign on the machine indicates that each cup contains at least 120ml of coffee. Calculate the probability that a cup of coffee dispensed by the machine will not meet this requirement to 4 dp 3) In order to be profitable, a cup must contain more than 115 ml of coffee but less than 145 ml of coffee. Calculate the probability that a cup of coffee dispensed by the machine will be profitable to 4 dp/nQuestion B3 [2 marks] You are advised to plot the graphs of the data given in Tables 1 and 2 below (on a separate spreadsheet) in order to answer the questions. TABLE 1 The data below shows the number of cars per minute entering a car park. Number of cars Frequency 0 4 1 2 3 4 5 6 7 8 17 26 32 19 10 4 2 1 TABLE 2 The data below shows the time taken, to the nearest minute, for employees at a clothing manufacturer to produce a shirt. Time (min) Frequency 17 18 19 3 10 18 20 21 22 23 24 25 26 27 28 29 30 31 29 43 53 55 52 41 26 18 13 8 5 2 First Second 1) Decide whether you think the following statements are TRUE or FALSE. "The data in TABLE 1 follow a Normal Distribution." "The data in TABLE 2 follow a Normal Distribution." If you think: First Second then Enter TRUE TRUE 1 TRUE FALSE 2 FALSE TRUE 3 FALSE FALSE 4 (1, 2, 3 or 4) 2) Use your graph for the data in TABLE 2 to determine, to the nearest minute, the mean time for an employee to produce a shirt./nQuestion B4 [2 marks] The marketing manager at a retailer wants to encourage customers to increase their spending. She knows that the amount customers spend is normally distributed with a mean of £65 and standard deviation of £14. 1) Customers who spent less than £M will be given 'money off vouchers'. If 18% of customers are in this category, find the value of M. 2) The top spending 14% of customers will be given 'VIP Customer Rewards'. Calculate the minimum spend required to qualify for these Rewards. Question B5 [2 marks] The profits of 200 franchises are normally distributed with a mean of £10200 and a standard deviation of £3700. to 2 dp to 2 dp 1) Calculate, correct to one decimal place, an estimate of how many franchises made a profit of £5000 or more. 2) The five most profitable franchises get a GoldStar award. Calculate, correct to the nearest pound, an estimate of the minimum profit required to get a GoldStar award. to 1 dp to nearest £

Fig: 1

Fig: 2

Fig: 3