#### ramasama

##### New Member
Hi people, Stasticians

I'm new and a mom. I have been asked to help out with an assignment due tomorrow :O - she has been away overseas for familial obligations and it's been many many moons since I studied Stats myself.

Please help, I really just want to know HOW to work out these problems, I would greatly appreciate it. Thank you so much

8 traffic lights on way to work
Traffic lights work independent of each other, probability of stopping at any one set is 0.4
If I stop at more than 6 I am late for work.

My friend arrives for tea in the mornings, usually at a mean of 09:30 and std deviation of 18 minutes.

1.
On any particular day, what is the probability she will arrive between 0900hrs and 1000hrs?

2.
If she arrives later, she is late. She s late 20% of the time.

What is the latest time she can arrive without being late?

Oranges are considered underweight if under 30grams. Their weight are independent and normally distributed at a mean of 32grams and std deviation of 2grams.

I buy two. What is the chance they are both underweight?

PLEASE YOUR HELP WOULD BE GREATLY APPRECIATED. I just want to learn how to work them, I'm reading all I can but it's cumbrous and further impeded by outside factors. Please help, thank you

#### statsguy

##### New Member
Hi people, Stasticians

I'm new and a mom. I have been asked to help out with an assignment due tomorrow :O - she has been away overseas for familial obligations and it's been many many moons since I studied Stats myself.

Please help, I really just want to know HOW to work out these problems, I would greatly appreciate it. Thank you so much

8 traffic lights on way to work
Traffic lights work independent of each other, probability of stopping at any one set is 0.4
If I stop at more than 6 I am late for work.

Let X be the number of stoplights that stop you on your way to work. X~Bin(8, 0.40). That is, X follows the binomial distribution with n = 8, p = 0.40. Then the probability that you are late is P(X=7) + P(X = 8). To compute these, use the binomial pmf:

P(X = 7) = (8 choose 7) * (.40^7) * (.60^1) = 8*(.60)*(.40^7)

p(X = 8) = (8 choose 8) * (.40^8) * (.60^0) = .40^8

My friend arrives for tea in the mornings, usually at a mean of 09:30 and std deviation of 18 minutes.

1.
On any particular day, what is the probability she will arrive between 0900hrs and 1000hrs?

What is the distribution of her arrival times? I'm guessing normal? Also "usually at a mean of 9:30" doesn't really make sense in probability terms FYI.

2.
If she arrives later, she is late. She s late 20% of the time.

What is the latest time she can arrive without being late?

Oranges are considered underweight if under 30grams. Their weight are independent and normally distributed at a mean of 32grams and std deviation of 2grams.

I buy two. What is the chance they are both underweight?

Let X be the probability that an orange is underweight. Then, by independence, the probability that both are overweight is P(X<30)^2. For an observation of 30 grams, Z = (30 - 32)/2 = -1. So the probability that an orange is underweight is P(Z < -1), where Z ~ N(0,1). Using R, P(Z < -1) = .16, so the probability that both are underweight is .16^2 = 0.026.

PLEASE YOUR HELP WOULD BE GREATLY APPRECIATED. I just want to learn how to work them, I'm reading all I can but it's cumbrous and further impeded by outside factors. Please help, thank you
Hope this helps!