Question 1 _____________________________________________________________________________ a) On average 2.5 faulty reports are made to a company’s switchboard per day. i. Name the random variable present in this problem and state its distribution. Calculate the probability that ii. FOUR faulty reports will be made on Monday iii. Less than 3 faulty reports in a 5-day work week b) The number of attempts at shooting goals made by a netballer in a tournament can be modelled by a binomial distribution with a probability of success equal to 0.35. (i) In a sample of 12 attempts at shooting goals, calculate the probability that EXACTLY 4 were successful. (ii) Given that the netballer made a total of 120 attempts at shooting goals in a tournament, calculate the expected number of successful shoots. Question 2 _____________________________________________________________________________ a) A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter, ?̅ = 14.9 mm and a standard deviation, s = 1.33 mm. A test was carried out at the 5% level of significance to determine whether the machine is in good working order. Assume that the diameter of the disc follows a normal distribution. i. State, in symbols, the null and alternate hypotheses for this test. ii. State, with reasons, whether a t-test or a z-test will be appropriate. iii. (Determine the rejection region(s) of the test. iv. Calculate the value of the test statistic. v. State, with reason, a valid conclusion for the test.
Question 1
_____________________________________________________________________________
a) On average 2.5 faulty reports are made to a company’s switchboard per day.
i. Name the random variable present in this problem and state its distribution.
Calculate the probability that
ii. FOUR faulty reports will be made on Monday
iii. Less than 3 faulty reports in a 5-day work week
b) The number of attempts at shooting goals made by a netballer in a tournament can be modelled by a binomial distribution with a probability of success equal to 0.35.
(i) In a sample of 12 attempts at shooting goals, calculate the probability that EXACTLY 4 were successful.
(ii) Given that the netballer made a total of 120 attempts at shooting goals in a tournament, calculate the expected number of successful shoots.
Question 2
_____________________________________________________________________________
a) A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discs gave a mean diameter, ?̅ = 14.9 mm and a standard deviation, s = 1.33 mm. A test was carried out at the 5% level of significance to determine whether the machine is in good working order.
Assume that the diameter of the disc follows a
i. State, in symbols, the null and alternate hypotheses for this test.
ii. State, with reasons, whether a t-test or a z-test will be appropriate.
iii. (Determine the rejection region(s) of the test.
iv. Calculate the value of the test statistic.
v. State, with reason, a valid conclusion for the test.
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