Question

1) A researcher reports that when groups of four children are randomly selected from a population of couples meeting certain criteria, the probability distribution for the number of girls, ?, is given in the following table where ? is a positive constant.

x	?(?)	?(? ≤ ?)
0	0.4	?
1	?	?
2	3? − 0.2	?
3	2?	?
4	0.2	?

a) Find ?(2).
b) Complete the column of cumulative probability. (Please rewrite the table in your answer sheet) c)What is the probability of getting at least one girl?
d) What is the probability of getting more than one and less than three girls?
e) What is the probability of getting at most three girls?
f) What are the mean, the variance and the standard deviation of ??

7) The lengths of pregnancies are normally distributed with a mean of 250 days and a standard deviation of 10 days.

a) Find the probability of a pregnancy lasting less than 270 days.

b) If we stipulate that a baby is premature if the length of pregnancy is the lowest 3%, find the length that separates premature babies from those who are not premature.

8) The response time of a fire department in an emergency call is the period between the time the call is received by the dispatcher and the time the first truck service arrives on the scene. It was found that the response time follows a normal distribution with mean of 10 min and standard deviation of 3 min. What is the probability that the response time is exactly equal to 17.5 min?

Answer 1

dear student lease post the question one at a time.

7) For the probability distribution to be valid.

.......(1)

Hence .......(2)

Using 1 and 2

now

a)P(2) = 3k-0.2=3(0.1)-0.2=0.1

b)

x	p(x)
0	0.4	0.4
1	0.1	0.5
2	0.1	0.6
3	0.2	0.8
4	0.2	1

c) The probability of getting at least one girl is

d) the probability of getting more than one and less than three girls = Probability of getting 2 girls = 0.1

e) the probability of getting at most three girls =

f) Mean =

standard deviation =