Answer all the questions given below

INSTRUCTION: ANSWER ALL QUESTIONS 11 Define the following Probability distribution Random variable 21 0 Find the standard deviation for the given data : 2 5. 3, 3 3, 4, 4.2, 5, 3 ") Let a continuous random variable X follow normal distribution N(4 0, 16) Find Pr(X > 4.6) bi A study is done on a sample of to students and the average revision time is found to be 3 Hours with a standard deviation of 2.3 hours, Find the probability that the sample mean lime allocated per week for revision in less than six hours Athume time allocated in normally distributed 3) A MTN telephone company claims that the average length of a phone call is 8 minutes, Ina random sample of 58 phone calls, the sample mizan was 7.8 minutes and the standard deviation the 0.5 minutes. Write the appropriate the null and alternative hypothesis for the claim made 4) A family has three children, Given that a random variable X, is defined as observing a boy child, find i) The probability distribution of X The expected value The probability of observing at least one child