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Probabilities of Life Insurance Purchase

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In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant binomial distribution, answer the following questions;
a) What is the probability that exactly 5 customers will buy life insurance from this agent in the coming month?

b)What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?

c)What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?

Please use the attached Excel sheet to assist and use the BINOMDIST function in the Excel.

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Solution Summary

This solution computes the probability of a specified number of customers purchasing life insurance in the coming month in 3 different scenarios.

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In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant binomial distribution, answer the following questions;
a) What is ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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