There are 1000 pupils in a school. Find the probability that exactly 3 of them have their birthdays on 1 January, by using (a) B(1000, 1/365) (b) Po(1000/365) There are 5000 students in a university. Calculate the II probability that exactly 15 of them have their birthdays on 1 January by using (a) suitable binomial distribution approximation III (a) In a certain school, 30% of the students are in the age (b) suitable Poisson group 16-19. i Ten students are chosen at random. What is the probability that fewer than four of them are in the 16-19 age group? ii if the ten students were chosen by picking ten who were sitting together at lunch, explain why a binomial distribution might no longer have been suitable. (b) A factory makes large quantities of coloured sweets and it is known that on average 20% of the sweets are coloured green. A packet contains 20 sweets. Assuming that the packet forms a random sample of the sweets made by the factory, calculate the probability that exactly seven of the sweets are green. If you knew that, in fact, the sweets could have been green, red, orange or brown, would it have invalidated your calculation? IV (a) Find the mean of the random variables X and Y which have the following probability distribution (i) P(X = x) (ii) P(Y = y) (b) The random variable T has the probability distribution given in the following table 1 2 3 4 1/8 3/8 1/8 ¼ 1/8 X y -2 -1 1 2 3 0.15 0.25 0.3 0.05 0.2 0.05 1 3 4 6. 7 0.1 P (T= t) Find E (T) and Var (T) V Given that X - N (44, 25), find s, t, u and v (a) P (X< s) = 0.9808 (b) P(X > t) = 0.7704 (c) P(X > u) = 0.0495 (d) P(X< v) = 0.3336 0.2 0.1 0.2 0.1 0.2 0.1 VI X has normal distribution and P(X>73.05) = 0.0289. Given that the variance of the distribution is 18, find the mean.
There are 1000 pupils in a school. Find the probability that exactly 3 of them have their birthdays on 1 January, by using (a) B(1000, 1/365) (b) Po(1000/365) There are 5000 students in a university. Calculate the II probability that exactly 15 of them have their birthdays on 1 January by using (a) suitable binomial distribution approximation III (a) In a certain school, 30% of the students are in the age (b) suitable Poisson group 16-19. i Ten students are chosen at random. What is the probability that fewer than four of them are in the 16-19 age group? ii if the ten students were chosen by picking ten who were sitting together at lunch, explain why a binomial distribution might no longer have been suitable. (b) A factory makes large quantities of coloured sweets and it is known that on average 20% of the sweets are coloured green. A packet contains 20 sweets. Assuming that the packet forms a random sample of the sweets made by the factory, calculate the probability that exactly seven of the sweets are green. If you knew that, in fact, the sweets could have been green, red, orange or brown, would it have invalidated your calculation? IV (a) Find the mean of the random variables X and Y which have the following probability distribution (i) P(X = x) (ii) P(Y = y) (b) The random variable T has the probability distribution given in the following table 1 2 3 4 1/8 3/8 1/8 ¼ 1/8 X y -2 -1 1 2 3 0.15 0.25 0.3 0.05 0.2 0.05 1 3 4 6. 7 0.1 P (T= t) Find E (T) and Var (T) V Given that X - N (44, 25), find s, t, u and v (a) P (X< s) = 0.9808 (b) P(X > t) = 0.7704 (c) P(X > u) = 0.0495 (d) P(X< v) = 0.3336 0.2 0.1 0.2 0.1 0.2 0.1 VI X has normal distribution and P(X>73.05) = 0.0289. Given that the variance of the distribution is 18, find the mean.
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Transcribed Image Text:21 I There are 1000 pupils in a school. Find the probability that
exactly 3 of them have their birthdays on 1 January, by using
(a) B(1000, 1/365)
(b) Po(1000/365)
II
There are 5000 students in a university. Calculate the
probability that exactly 15 of them have their birthdays on 1
January by using
(a) suitable binomial distribution
approximation
III (a) In a certain school, 30% of the students are in the age
(b) suitable Poisson
group 16-19.
i Ten students are chosen at random. What is the probability
that fewer than four of them are in the 16-19 age group?
ii if the ten students were chosen by picking ten who were
sitting together at lunch, explain why a binomial distribution
might no longer have been suitable.
(b) A factory makes large quantities of coloured sweets and it is
known that on average 20% of the sweets are coloured green. A
packet contains 20 sweets. Assuming that the packet forms a
random sample of the sweets made by the factory, calculate the
probability that exactly seven of the sweets are green. If you
knew that, in fact, the sweets could have been green, red, orange
or brown, would it have invalidated your calculation?
IV (a) Find the mean of the random variables X and Y which
have the following probability distribution
(i) х
P(X = x)
(ii)
P(Y= y)
(b) The random variable T has the probability distribution given
in the following table
1 2 3 4
1/8 3/8 1/8 4 1/8
y
-2
-1
1
3
0.15 0.25
0.3 0.05 0.2 0.05
t
1
2
3
4
5
7
P (T= t)
Find E (T) and Var (T)
V Given that X - N (44, 25), find s, t, u and v
(a) P (X< s) = 0.9808 (b) P(X > t) = 0.7704 (c) P(X > u) =
0.0495 (d) P(X < v) = 0.3336
0.1 0.2
0.1
0.2 0.1
0.2
0.1
VI X has normal distribution and P(X>73.05) = 0.0289. Given
that the variance of the distribution is 18, find the mean.
BY B.E.F
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