12 Let X be a binomial random variable with n = 25 and p = 0.05. (a) Use the binomial probabilities table to find P(X = 0), P(X = 1) and P(X = 2). (b) Approximate the three probabilities in part (a) using the appropriate Poisson distribution. 13 The number of calls received by a switchboard operator between 9 and 10 a.m. has a Poisson distribution with a mean of 12. Find the probability that the operator received at least five calls during the following periods: (a) Between 9 and 10 a.m. (b) Between 9 and 9:30 a.m. (c) Between 9 and 9:15 a.m. 14 The marketing manager of a company has noted that she usually receives 10 complaint calls from customers during a week (consisting of 5 working days) and that the calls occur at random. Find the probability of her receiving exactly 5 such calls in a single day. 15 Use the standard normal probability table to find the following: (a) P(X ? 1.7) (b) P(Z ? -0.95) (c) P(X ? -1.96) (d) P(-1.14 ? Z ? 1.55)
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Step 1: Identify the parameters given in the problem: - Average rate of complaints: 10 per five working days - Number of complaints in a single day: 5 Show more…
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1. Assume X has a binomial distribution. Use the binomial formula, tables, or technology to calculate the probability of the indicated event: a. n=23, p=0.5 P(11 ≤ X ≤ 14) = Round to four decimal places if necessary b. n=18, p=0.4 P(6 < X < 9) = Round to four decimal places if necessary 2. A bank manager sees an average of 5.2 new clients in her office every day. If the clients arrive at random throughout the day, determine the probability that she will see 4 clients in her office in the first half of the day today. Analyze the given scenario and complete the following: a. Determine which probability distribution should be used to model the scenario. Hypergeometric, Geometric, or Poisson? b. Calculate the probability of the indicated event. P(x)= Round to 3 significant digits c. Determine the expected value and variance of the random variable. E(X) = Variance = Round to 3 significant digits
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