Assignment
Q1. A restaurant records the number of customers it receives for 15 days. The data is shown in the following.
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140, 141, 171, 178, 187, 140, 238, 247, 254, 297, 205, 211, 206, 286, 187
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a. Calculate the Q2, D6, D3, Q1 for these data.
b. Draw the boxplot for this data.
c. Calculate Software Skewness for this data. Show all steps of calculation.
Q2. We roll a dice two times and observe the sum of numbers that the dice shows at all three rolls:
a. What is the experiment?
b. What are the outcomes? How many outcomes do we have?
c. What is the probability that the sum of the outcomes is 4?
d. What is the probability that the sum of the outcomes is 6?
e. What is the probability that the sum of the outcomes is less than 5?
Q3. A restaurant manager records the number of customers walk-in between 5:00 PM and 10:00 PM each day for 2 weeks. Data is showing as follows:
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18, 25, 15, 24, 38, 33, 26, 13, 27, 32, 24, 31, 25, 19
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a. What is the probability of seeing at least one customer entering the restaurant between 5:00 PM and 10:00 PM?
b. What is the probability of seeing exactly one customer entering the restaurant between 5:00 PM and 10:00 PM?
c. What is the probability of seeing no customer entering the restaurant between 5:00 PM and 10:00 PM?
d. What is the probability of seeing at most two customers entering the restaurant between 5:00 PM and 10:00 PM?
Q4. The following table shows the probability of different numbers of customer entering a very small restaurant.
a. Calculate mean and variance of the discrete random variable.
b. Use Excel to calculate variance and mean of the discrete random variable.
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# Customers
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Probability
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0
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0.15
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1
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0.20
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2
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0.30
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3
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0.20
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4
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0.15
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Q5. A traffic camera recorded the number of cars passing an intersection between 2:00 AM and 5:00 AM each day for 14 days. Data is showing as follows:
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10, 15, 13, 14, 18, 23, 21, 18, 17, 12, 21, 11, 30, 29
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a. What is the probability of seeing at least one car passing the intersection between 2:00 AM and 5:00 AM?
b. What is the probability of seeing exactly one car passing the intersection between 2:00 AM and 5:00 AM?
c. What is the probability of seeing no car passing the intersection between 2:00 AM and 5:00 AM?
d. What is the probability of seeing at most 2 cars passing the intersection between 2:00 AM and 5:00 AM?
Q6. Customers arrive at the carwash uniformly from 2 minutes to 50 minutes, on the weekend.
a. How long the washing station should be idle until a customer arrives? (What is the mean)
b. What is the probability that the washing station has to be idle more than 20 minutes?
c. What is the probability that the washing station has to be idle between 15 and 45 minutes?