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A large number of people are waiting in line at Espresso Royale (as it often happens at around noon). The barista announces that he will start asking for each person's birthday, one by one, and the first person in the line whose birthday happens to coincide with one of the previous people will receive a free drink. Which position in the line has the highest chance of success?
Make the usual assumptions about independence of birthdays and 365 days in a year. If, e.g., you think that the third person in the line has the highest chance of success, enter 3 as your answer. (Hint: if n?2 is an integer, find a formula for the probability that the n-th person in the line will have the first duplicate birthday. Then write a simple program to find where the maximum is.)
The probability that you win is 6/36=1/6, and P(loss) = 5/6. Find a rough range for a) 200 plays, (b) 20, 000 plays. You must show your work when you compute the SD of the box.
What are the optimal values of A and B? What is the minimum cost and if the cost of B could be reduced to $42 per unit, how many units of B would be optimal? What would the minimum cost be?
We can think of this as the value of mew that maximizes f(y), the probability that our observed value of y occurs.
the machining center at a production facility has three lathes of differing ages and thus precision. the oldest machine
A survey of the number of calls received by a sample of Southern Phone Company subscribers last week revealed the following information.
Assume the population standard deviation is 7.1 mpg. State the correct null and alternative hypotheses that the company wishes to test. Calculate the test statistic that would be used for conducting the desired test.
Setup Null and Alternate hypotheses to test if average amount of soda in each can is less than 32 oz. Test the hypothesis using a = 0.05. What can you conclude from all this?
a fair coin is tossed 500 times. find the probability of obtaining more than 300
What is the probability that the drug will be effective for 2 hours or less?
In the Willow Brook National Bank waiting line system (see Problem 1), assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour or 0.6 customer per minute.
The average salary for graduates entering the actuarial field is $40,000. If the salaries are normally distributed with a standard deviation of $5,000, find the probability that An individual graduate will have a salary over $45,000.
How does the shape of the quantile plot affect your interpretation of the results?
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