1). Primary healthcare workers believe that anaphylactic shock reaction to immunization injections occurs with children in one case in two thousand. Immunization teams carry adrenalin packs in order to treat children suffering a shock reaction. Calculate, using Minitab, the probability that two adrenalin packs would be insufficient to treat the shock reactions occurring in a group of 1200 children.
2). Customers of a mortgage bank expect to have mortgage applications processed within 35 working days of submission. Given that the processing time at the bank can be modelled by the N (28, 32) distribution, verify that 99% of applications would be processed within 35 working days. Following a successful Six Sigma project aimed at reducing processing time, it was found that, although variability in processing time was unchanged, the mean had dropped to 19 working days. The bank wishes to inform prospective customers that '99 times out 100 we can process your application in q working days'. Assuming that the normal distribution is still an adequate model, calculate q.
3). Use of the symbol Z for a random variable having the standard normal distribution i.e. the N(0,1) distribution, is fairly widespread. Many statistical texts use the notation zp for the value such as P(Zp) = 1 - p . Thus for the case of p = 0.1, 1 -p = 0.9, the required value may be obtained using Calc > Probability Distributions > Normal ... with the Inverse cumulative probability option.
- Use Minitab to generate the worksheet in Figure 4.41. In order to round the values of zp to two decimal places click on a cell in the column containing the values to be rounded. Next use Editor > Format Column > Numeric... , select Fixed decimal and change the number of decimal places to 2.
4). A single-sample acceptance attributes sampling plan is required to have a producer's risk of 0.06 for an acceptable quality level of 0.5% nonconforming, and a consumer's risk of 0.10 for a rejectable quality level of 5% nonconforming. Use Minitab to determine the appropriate plan.