Download hw 6 (s2) set wc 19th Sept 17/11/2016 11:04:58 Word Document 31.5

HW 6: Statistics 2.
BINOMIAL DISTRIBUTION
Total= 35 marks
1a) If X ῀ B(25, 0.3), use the binomial tables to find the probability that X is exactly
i)
6
ii)
7
iii)
8
iv)
9
(4 marks)
b) State the mode of X.
(1 mark)
c) Give the mean and variance of X.
(2 marks)
2) It is estimated that 4% of people have green eyes. In a random sample size of n, the expected number of people
with green eyes is 5.
a) Calculate the value of n.
(1 mark)
b) The expected number of people with green eyes in a second random sample is 3. Find the standard deviation of
the number of people with green eyes in this second sample.
(2 marks)
3) Each evening Louise sets her alarm clock for 7.30am. She believes that the probability that she wakes before her
alarm rings each morning is 0.4 and is independent from day to day.
a) Assuming that Louise’s belief is correct, calculate the probability that during a week (5 mornings), she wakes
before her alarm rings
i) on 2 or fewer mornings
ii) on more than 1 but fewer than 4 mornings
(4 marks)
b) Assuming that Louise’s belief is correct, calculate the probability that during a 4-week period, she wakes before
her alarm clock rings on exactly 7 mornings.
(4 marks)
c) Assuming that Louise’s belief is correct, calculate values for the mean and standard deviation of the number of
mornings in a week when Louise wakes before her alarm clock rings.
(2 marks)
d) During a 50-week period, Louise records, each week, the number of mornings on which she wakes before her
alarm rings. The results are as follows:
Number of
mornings
Frequency
0
1
2
3
4
5
10
11
9
9
6
5
i) Calculate the mean and standard deviation of these data.
(6 marks)
ii) State, giving reasons, whether your answers to part di support Louise’s belief that the probability that she
wakes before her alarm rings each morning is 0.4 and is independent from morning to morning.
(2 marks)
4) Copies of an advertisement for a course in practical statistics are sent to mathematics teachers in a county. For
each teacher who receives a copy, the probability of subsequently attending the course is 0.07.
Eighteen teachers receive a copy of the advertisement. What is the probability that the number who subsequently
attend the course will be
a) 2 or fewer
b) exactly 4?
(7 marks)