please help me solve these problem

To check the accuracy of a particular weather forecaster, records were checked only for those days when the forecaster predicted rain "with 40% probability." A check of 15 of those days indicated that it rained on 8 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? P = (b) What are the mean u and standard deviation o of x, the number of days on which it rained, assuming that the forecaster is accurate? (Round your standard deviation to two decimal places.) days O = days (c) Calculate the z-score for the observed value, x = 8. [HINT: Recall that z-score = (x - M)/o.] (Round your answer to two decimal places.) Z =Letx be a binomial random variable with n = 5, p = 0.4. Find the following values. (Round your answers to three decimal places.) (a) P(X = 4) P(X = 4) = 0.990 x (b) P(X s 1) P(X s 1) = 0.999 x (c) P(X > 1) P(X > 1) = 0.999 X (d) u =np (e) a = xpq You may need to use the appropriate appendix table or technology to answer this question. Consider a binomial random variable with n = 6 and p = 0.8. Let x be the number of successes in the sample. (Round your answers to three decimal places.) (a) Find the probability that x is 3 or less. 0.099 (b) Find the probability that x is 3 or more. 0.099 (c) Find P(x 2) (d) P(2 5 x 5 4)LetX be a binomial random variable with n = 20 and p = 0.1. (a) Calculate P(X S 5) using Table 1 in Appendix I to obtain the exact binomial probability. (Round your answer to three decimal places.) P(X s 5) = 1 X (b) Use the Poisson approximation to calculate P(X S 5). (Round your answer to three decimal places.) P(X S 5) = 1 x (c) Compare the results of parts (a) and (b). Is the approximation accurate? 0 Yes, the difference between the values in parts (a) and (b) is less than 0.01. C? No, the difference between the values in parts (a) and (b) is at least 0.01. I You may need to use the appropriate appendix table or technology to answer this