# Probability and percentiles

#### andy35

##### New Member
An airline has found from past experience that the weight of checked-in baggage items is Normally distributed with mean 13 kg and standard deviation 3.1 kg.

a)What is the probability that a randomly selected baggage item weighs more than 15kg?

This is what I have come up with;
To Get Z = (data point - mean) / standard deviation
Z = (15-13) / 3.1
Z = 0.645
P( X > 0.645) = 0.740

b)What is the probability that a sample of 10 baggage items weighs more than 150kg in total?

c)What is the 80th percentile of checked-in baggage weight (such that 80% of baggage items weigh less than this amount).

This is my work so far for this question, I got the answer out from doing the calcs in the computer system they have asked us to use but Im not sure how to work it out myslef with a formula.
P ( X < a) = 0.80

P (X < 0.80) = 15.61

Again, I dont know where to begin with this A random sample of 30 baggage items resulted in a mean weight of 13.544 kg and standard deviation 2.709 kg. Find 95% confidence intervals for
i. the population mean weight.
ii. the population standard deviation of weight.

Any assistance would be very much appreciated. Thank you