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state two conditions for the function f(x,y) to be a continuous joint probability distribution of the continuous random variable x and y
Clearly show how you draw a conclusion when you test this hypothesis, using both methods, i.e.
(a) critical value approach, and (b) p-value approach
The table below show Business statistics I examination marks for a class of one hundred students .
Marks 10-19 (4 student )
20-29 ( 8 student )
30-39 ( a - student )
40-49 ( 22 student )
50-59 ( 48 student )
60-69 ( b - student )
The mean score of the students was 46.5
(i) Show that the values of a and b are 12 and 6 respectively. (5marks)
(ii) Estimate the median for the above sample. (3marks)
(iii) Determine the variance and the standard deviation (4 marks)
(iv) Given that 32% of the students failed the examination, what was the cut off points.
(3 marks)
(v)Estimate the mode for this data. (3marks)
Suppose that weekly demand for the electronic toy of a company is normally
distributed, with a mean of 2400 units and a standard deviation of 280 units.
i) What is the probability that the weekly demand for the electronic toy is
between 2350 and 2670?
ii) What is the value of a constant k, if
P(X > k) = 0.70
Accuracy in taking orders at a drive-through window is important for fast-food chains.
Each month, QSR Magazine, www.qsrmagazine.com, publishes the results of its
surveys. Accuracy is measured as the percentage of orders that are filled correctly. In
a recent month, the percentage of orders filled correctly at McDonald’s was
approximately 91%. Suppose that you and ten friends go to the drive through window
at McDonald’s and independently place orders,
i. what is the probability that at least 7 orders will be filled correctly?
ii. what is the probability that between 3 and 9 orders will be filled
correctly?
iii. what is the probability that not more than 5 orders will NOT be filled
correctly?
11. The battery life of a certain battery is normally distributed with a mean of 90 days and a standard deviation of 3 days.
For each of the following questions, construct a normal distribution curve and provide the answer.
a) About what percent of the products last between 87 and 93 days?
b) About what percent of the products last 84 or less days?
c) For each of the following questions, use the standard normal table and provide the answer.
d) About what percent of the products last between 89 and 94 days?
e) About what percent of the products last 95 or more days?
A shop sells five pieces of shirt every day, from 10am to 10pm.
i) What is the probability of selling more than three shirts today?
ii) What is the probability of selling at most thirty-one shirts from Monday to
Thursday?
iii) What is the probability of selling three to eight shirts for 9 hours?
