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A woman working in telemarketing makes telephone calls to private homes according to a Poisson process with rate λ = 100 per (working) day. We estimate that the probability that she succeeds in selling her product, on a given call, is equal to 5%, independently from one call to another. Let N(t) be the number of telephone calls made in the interval [0, t], where t is in (working) days, and let X be the number of sales made during one day.
(a) Suppose that the woman starts her working day at 9 a.m. and stops working at 7 p.m. Let TQ be the number of minutes between 9 a.m. and the moment of her first call of the day, and let SQ be the duration (in minutes) of this call. We suppose that SQ ~ Exp(l) and that TQ and 5o are independent random variables. What is the probability that the woman has made and finished her first call at no later than 9:06 a.m. on an arbitrary working day?
(d) What is the probability that the woman will make no sales at all on exactly one day in the course of a week consisting of five working days?
Assume independent events. Why might the assumption of independence be violated? (b) Why might a driver be tempted not to use a seat belt "just on this trip"?
What is the z score for a GRE score of 597? What is the percentile rank of this z score and What is the height (in inches) that marks the 75th percentile for this group of officers?
(a) What is the average number of customers in the shop? (b) What is the proportion of potential customers that enter the shop? (c) If the barber could work twice as fast, how much more business would he do?
You read that statistical test at α=0.01 level has probability 0.14 of making a Type II error when specific alternative is true. Calculate the power of test against this alternative?
A company's headquarters is located in downtown Chicago. The company is interested to know the mean driving time of its employees if they require their employees to start working at 6:00 am. Fifty employees are randomly sampled over four weeks and..
some studies have shown that in the united states men spend more than women buying gifts and cards on valentines day.
Elucidate correlation coefficient of determination R-square also Adjusted R-square. A computer utility was implimentated to the data collected in a study of a generalized health.
Show that there is no rational number b/a whose square is 2, as follows: if b^2 = 2a^2, then b is even, so b = 2c, so, substituting and cancelling 2, 2c^2 = a^2.
Getting data and making calculations can be the easy part. Understanding the real issues and asking the right questions can be more difficult. Reporting average travel time or the variability in competitors' price can be a computational exercise.
a. Approximately what proportion of overweight children has left atrial diameters less than 25 mm? b. Approximately what proportion of overweight children has left atrial diameters greater than 32 mm?
What is the probability that more than 25% of the business travelers say that the reason for their most recent business trip was an internal company visit?
The probability that a male will be color blind is 0.042. Use the normal curve approximation to the binomial distribution to find the probabilities that in a group of 53 men, no more than 6 are color-blind.
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