3.1.7A flu virus hits a company employing 180 people. Independent of the other employees, there is a probability of p = 0.35 that each person needs to take sick leave. What are the expectation and variance of the proportion of the workforce who need to take sick leave? In general, what value of the sick rate p produces the largest variance for this proportion?
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- 6.36. Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in 1 week is given by the following table: 1 2 3 4 7 8 p(z) 0.05 0.10 0.12 0.30 0.30 0.11 0.01 0.01 a. Find the mean value of æ (the mean number of systems sold). b. Find the variance and standard deviation of æ. How would you interpret these values? c. What is the probability that the number of systems sold is within 1 standard deviation of its mean value? d. What is the probability that the number of systems sold is more than 2 standard deviations from the mean?Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 148 millimeters, and a variance of 25. If a random sample of 50 steel bolts is selected, what is the probability that the sample mean would be less than 147.1 millimeters? Round your answer to four decimal places.Suppose a life insurance company sells a $240,000 1-year term life insurance policy to a 20-year-old female for $290. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. The expected value of this policy to the insurance company is $180.56. What is the standard deviation of the value of the life insurance policy? Why is the value so high?
- Suppose a life insurance company sells a $170,000 1-year term life insurance policy to a 20-year-old female for $170. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. The expected value of this policy to the insurance company is $92.48. What is the standard deviation of the value of the life insurance policy? Why is the value so high?Suppose that the annual rate of return for a common biotechnology stock is normally distributed with a mean of 5% and a standard deviation of 6%. Find the probability that the one-year return of this stock will be positive. Round your answer to at least four decimal places.A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 15 years with a variance of 25. If the claim is true, in a sample of 41 wall clocks, what is the probability that the mean clock life would be less than 15.4 years? Round your answer to four decimal places
- Suppose a life insurance company sells a $170,000 1-year term life insurance policy to a 20-year-old female for $300. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. The expected value of this policy to the insurance company is$222.48. What is the standard deviation of the value of the life insurance policy? Why is the value so high? Part 1 The standard deviation of the value of the life insurance is $estions 1. Residents of rural Wisconsin drink an average of 4L of soda per week, with a standard deviation of 1L. What is the probability that a randomly-selected resident of rural Wisconsin drinks 5.5 to 6.8L of soda per week?It has been found that 15% of customers at a particular restaurant wait longer than 35 minutes for their order. We assume normal distribution, and randomly select 105 customers. Q.3.2.1 Determine the standard error for this sample. Q.3.2.2 What is the probability that, for the sample of 105 customers, the proportion who wait longer than 35 minutes for their order is greater than 15.75%? Interpret your answer.