Kelly throws a tetrahedral die n times and records the number on which it lands for each throw.
She calculates the expected frequency for each number
... [Show More] to be 43 if the die was unbiased.
The table below shows three of the frequencies Kelly records but the fourth one is missing.
Number 1 2 3 4
Frequency 47 34 36 x
(a) Show that x = 55
(1)
Kelly wishes to test, at the 5% level of significance, whether or not there is evidence that the tetrahedral die is unbiased.
(b) Explain why there are 3 degrees of freedom for this test.
(1)
(c) Stating your hypotheses clearly and the critical value used, carry out the test.
(5)
_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
*P66799A0224*
Question 1 continued
_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 7 marks)
*P66799A0324*
2. On a weekday, a garage receives telephone calls randomly, at a mean rate of 1.25 per 10 minutes.
(a) Show that the probability that on a weekday at least 2 calls are received by the garage in a 30‑minute period is 0.888 to 3 decimal places.
(2)
(b) Calculate the probability that at least 2 calls are received by the garage in fewer than 4 out of 6 randomly selected, non‑overlapping 30‑minute periods on a weekday.
(2)
The manager of the garage randomly selects 150 non‑overlapping 30‑minute periods on weekdays.
She records the number of calls received in each of these 30‑minute periods.
(c) Using a Poisson approximation show that the probability of the manager finding at least 3 of these 30‑minute periods when exactly 8 calls are received by the garage is 0.664 to 3 significant figures. [Show Less]