Question

Please provide all answers according to question numbers with steps thank you.

(9) To qualify for the RCMP recruits are tested for stress tolerance. The scores are normally distributed with mean = 66 and standard deviation = 8.

a) If only the top 45% of the recruits are to be chosen to continue the RCMP training, find the minimum score a recruit would need to continue the RCMP training.

b) Find the probability that the mean stress tolerance score for a random sample of 38 of these recruits is less than 63.

(10) Suppose that 30% of all commuters ride the train to work.

a) Find the probability that if 10 workers are selected, more than 2 will ride the train.

b) If 500 workers are selected, find the probability that at least 130 of them will ride the train. Use the normal approximation to the binomial distribution.

Answer 1

9)

a)

Let:

We need to calculate the following:

Minimum score required =67.008

b)

We know that:

We need to find:

10)

Let X be the no. of commuters who ride the train to work
Then X~Binomial(n,0.30)

Where n is the sample size.

a)

We need to find the probability:

P(X=0)	0.028248
P(X=1)	0.121061
P(X=2)	0.233474

Sum=0.3828

b)

If 500 workers are selected:

Since n is large we will use normal approximation:

We need to calculate the following:

Answer 2

9)

a)

Let:

We need to calculate the following:

Minimum score required =67.008

b)

We know that:

We need to find:

10)

Let X be the no. of commuters who ride the train to work
Then X~Binomial(n,0.30)

Where n is the sample size.

a)

We need to find the probability:

P(X=0)	0.028248
P(X=1)	0.121061
P(X=2)	0.233474

Sum=0.3828

b)

If 500 workers are selected:

Since n is large we will use normal approximation:

We need to calculate the following: