Most weather forecasters protect themselves very well by attaching probabilities to their forecasts, such as "The probability of rain today is 40%.\" Then, if a particular forecast is incorrect, you are expected to attribute the error to the random behaviour of the weather rather than to the inaccuracy of the forecaster. To check the accuracy of a particular forecaster, records were checked only for those days when the forecaster predicted rain \"with 30% probability.\" A check of 15 of those days indicated that it rained on 7 of the 15. (a) If the forecaster is accurate, what is the appropriate value of p, the probability of rain on one of the 15 days? (b) What are the mean ,u and standard deviation a of X, the number of days on which it rained, assuming that the forecaster is accurate? (Round your standard deviation to two decimal places.) (c) Calculate the Zescore for the observed value, X : 7. [HINT: Recall that Zescore : (X 7,010.] (Round your answer to two decimal places.) (d) Do these data disagree with the forecast of a \"30% probability of rain"? Explain. O The observed event is more than 2 standard deviations above the mean, so it is not unlikely assuming ,0 is accurate. 0 The Observed event is less than 2 standard deviations above the mean, so it is very unlikely assuming p is accurate. 0 The Observed event is more than 2 standard deviations above the mean, so it is unlikely assuming p is accurate. 0 The observed event is less than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate. A new surgical procedure is said to be successful 60% of the time. Suppose the operation is performed srx times and the results are assumed to be independent of one another What are the probabilities of these events? (Round your answers to three decimal places.) (a) all six operations are successful :I (b) exactly three are successful :I (c) less than two are successful :I You may need to use the appropriate appendix table or technology to answer this question. A normal random variable x has mean / = 6 and standard deviation o = 2. Find the probabilities associated with the following intervals. (Round your answers to four decimal places.) (a) 1.5 8.5 (c) Xso