Thank you so much for your help. In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.What are the chances that a person who is murdered actually knew the murderer? The answer to this question explains why a lot of police detective work begins with relatives and friends of the victim. About 65% of people who are murdered actually knew the person who committed the murder. Suppose that a detective file in New Orleans has 64 current unsolved murders. Find the following probabilities. (Round your answers to four decimal places.)(a) At least 35 of the victims knew their murderers 0.9668 ✗(b) At most 48 of the victims knew their murderers 0.9676 ✗(c) Fewer than 30 victims did not know their murderers 0.9668 ✗(d) More than 20 victims did not know their murderers 0.6870 ✗Explanation: This problem requires applying the normal approximation to the binomial distribution to estimate probabilities regarding whether murder victims knew their murderers. There are four cases presented, each with a calculated probability that is marked as incorrect (indicated by the ✗ symbol). **Understanding Probability with Insurance Claims**In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then, use the normal distribution to estimate the requested probabilities.**Problem Scenario:**"Do you try to pad an insurance claim to cover your deductible? About 37% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 126 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.)"**Questions and Answers:**1. **(a) Half or more of the claims have been padded** - Probability: 0.0001 ✖2. **(b) Fewer than 45 of the claims have been padded** - Probability: 0.3483 ✔3. **(c) From 40 to 64 of the claims have been padded** - Probability: 0.9061 ✔4. **(d) More than 80 of the claims have not been padded** - Probability: 0 ✖**Additional Resources:**- You can read more on how to solve these types of problems [here]. - Watch a helpful video tutorial [here].This exercise helps in understanding the practical application of statistical methods, particularly the use of normal distribution as an approximation for binomial probabilities.

Note: Thank you for the question. Since multiple questions are posted, according to our policy, we are answering the first question for you. If you need help with any other question, please re-post the question and mention the question number you need help with.Normal approximation to the binomial: From the given information, sample size, n = 64. The probability of success, p = 0.65. The probability of failure, q =1- 0.65 = 0.35. Since np (64×0.65=41.6) and nq (64×0.35=22.4) are greater than 5, normal approximation to the binomial can be done. Mean and standard deviation of the distribution: The mean and standard deviation are calculated as follows. Mean, µ= np = 64×0.65=41.6 Standard deviation, σ = Sqrt(npq)= sqrt(64×0.65×0.35) = 3.816. a. The probability that at least 35 of the victims knew their murderers is obtained from the calculations given below: P(X≥35) = P(X>34.5) (using continuity correction) =P(Z>((34.5-41.6)/3.816) (by standardizing) = P(Z>-1.86) =1- P(Z≤-1.86) = 1-0.0314 {From the standard normal table, P(Z≤-1.86) = 0.0314} =0.9686 The probability that at least 35 of the victims knew their murderers is 0.9686. The probability value obtained using the Excel formula, =1-NORM.DIST(34.5,41.6,3.816,1) will be 0.9686.b. The probability that at most 48 of the victims knew their murderers is obtained from the calculations given below: P(X≤48) = P(X≤48.5) (using continuity correction) =P(Z≤((48.5-41.6)/3.816) (by standardizing) = P(Z≤1.81) {From the standard normal table, P(Z≤1.81) = 0.9649} =0.9649 The probability that at most 48 of the victims knew their murderers is 0.9649. The probability value obtained using the Excel formula, =NORM.DIST(48.5,41.6,3.816,1) will be 0.9647.c. The probability that fewer than 30 of the victims knew their murderers is obtained from the calculations given below: P(X<30) = P(X≤29.5) (using continuity correction) =P(Z≤((29.5-41.6)/3.816) (by standardizing) = P(Z≤-3.17) {From the standard normal table, P(Z≤-3.17) = 0.0008} =0.0008 The probability that fewer than 30 of the victims knew their murderers is 0.0008. The probability value obtained using the Excel formula, =NORM.DIST(29.5,41.6,3.816,1) will be 0.0008. d. The probability that more than 20 of the victims knew their murderers is obtained from the calculations given below: P(X>20) = P(X>20.5) (using continuity correction) =P(Z>((20.5-41.6)/3.816) (by standardizing) = P(Z>-5.53) =1- P(Z≤-5.53) = 1-0.0000 {From the standard normal table, P(Z≤-5.53) = 0.0000} =1.000 The probability that more than 20 of the victims knew their murderers is 1.0000. The probability value obtained using the Excel formula, =1-NORM.DIST(20.5,41.6,3.816,1) will be 1.0000.