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A medical school has discovered a new test for hepatitis. Experimentation has shown that the probability of a positive test is 0.85 given that a person has hepatitis. The probability is 0.11 that the test is positive given that the person does not have hepatitis. Assume that in the general population the probability that a person has hepatitis is 0.05. What is the probability that a person chosen at random will:
not have hepatitis and have a negative test?
have a positive test?
have hepatitis given that the test is positive?
A company has developed a new battery. The engineer in charge claims that the new
battery will have better performance than that of the old battery. To test the claim, the
company selects a simple random sample of 90 old batteries and 65 new batteries. The old
batteries ran continuously for 190 minutes with a standard deviation of 32 minutes; the
new batteries, 200 minutes with a standard deviation of 45 minutes. Test the engineer’s
claim at 0:05 level of signi…cance.

Carrefour Hypermarket employs four cashiers in a certain store to serve its customers. Suppose that Cashier 1 has an average service time of 6 minutes, Cashier 2 has an average service time of 4 minutes, Cashier 3 has an average service time of 2 minutes, and Cashier 4 has an average service time of 3 minutes, respectively. Suppose also that the service times are exponentially distributed and independent from each

other.

Let T1 be the service time of Cashier 1, T2 be the service time of Cashier 2, T3 be the

service time of Cashier 3, and T4 be the service time of Cashier 4 (please use this notation

in your solutions).


Suppose on a given day Cashier 4 is on leave, and Cashier 1, Cashier 2, and Cashier 3 are serving their customers. A customer arriving at the cashier area finds all cashiers serving other customers and no one else is waiting. What is the expected service time for the customer?

A small company has a call center with two phone lines only.


Carrefour Hypermarket employs four cashiers in a certain store to serve its

customers. Suppose that Cashier 1 has an average service time of 6 minutes, Cashier 2 has an average service time of 4 minutes, Cashier 3 has an average service time of 2 minutes, and Cashier 4 has an average service time of 3 minutes, respectively. Suppose also that the service times are exponentially distributed and independent from each other.

Let T1 be the service time of Cashier 1, T2 be the service time of Cashier 2, T3 be the

service time of Cashier 3, and T4 be the service time of Cashier 4 (

-A customer arriving at the cashier area sees all cashiers serving other

customers and no one else is waiting. Let Tw be the time the customer waits before

getting served. Express Tw in terms of T1, T2, T3, and T4. How long the waiting time will

be on average?



A small company has a call center with two phone lines only. An average of 40 people per hour calls in for orders, and it takes an average of 2 minutes to handle a call. Interarrival time between call arrivals and time to serve calling customers is on phone are exponentially distributed. If there are more than two customers waiting to be served, a caller gets a busy signal and hangs up.

b)What is the average time that the phone lines stay idle?

c) Calculate the fraction of the time that the line will be busy?

d) Calculate the average number of customers on hold waiting to be answered


Suppose we take a sample of 200 Facebook profiles and found only 34 to be ghost profile.
What is the 95% CI for the proportion of Facebook ghost profile?
1. (0.1179 ; 0.2221)
2. (0.1169 ; 0.2231)
3. (0.1015 ; 0.2385)
4. (0.1263 ; 0.2137)
5. None of the above
The number of times the AI algorithm is successful at detecting fake news is normally distributed with a sample mean of 900 and the sample standard deviation of 30. Assume a sample osize of 100 was used.
What is the 99% confidence interval estimate for the population mean?
1. (862.6636 ; 937.3364)
2. (864.2155 ; 935.7845)
3. (892.1208 ; 907;8792)
4. (892.9062 ; 907;0938)
5. (892.2600 ; 907.7400)
The number of times the AI algorithm is successful at detecting fake news is normally distributed with a sample mean of 900 and the sample standard deviation of 30. Assume a sample size of 100 was used.
What is the 95% confidence interval (CI) estimate for the population mean?
1. ( 894.1002 ; 905.8800)
2. (894.0474 ; 905.9526)
3. (852.8959 ; 947.1041)
4. (869.9665 ; 930.0335)
5. (895.0194 ; 904.9806)
An Insurance company offers to pay Php 400,000 for the damages incurred, while the policy costs Php 10,000. The probability that the company will need to pay the amount of insurance is 0.3%. Complete the probability distribution below to find the expected value.
A medical researcher wants to investigate the amount of time it takes for patients’ headache to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She believes that the population is normally distributed with a standard deviation of 20 minutes. How large a sample should she take to estimate the mean time tow within 1 minute with 90% confidence
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