Mathematics Probability

Question

An average of 5 customers come to the shop every half hour. Find the probability that exactly two customers will come to the shop during a given hour

2. The life span of an automatic washer is approximately normally distributed with mean and standard deviation equal to 3.1 and 1.2 years respectively. If this type of washer is guaranteed for 1 year what fraction of original sales will require replacement

3. Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15 find the probability that x assumes a value

I) less than 43

ii) greater than 74

iii) between 56 and 71

Answer 1

Hi Cynthia C.,

I'll say a bit for the first question. The other 2 parts are pretty cut-and-dried probability, just use the correct tables (and know which those are!)

So for the first: the expected, average visitors for 2 successive 1/2 hour periods is 5 x 2 = 10. So you need a Poisson distribution. (The mathematician, not the French fish). If this is a new concept to you: it's like a binomial distribution, but it can only run upwards from 0. No negative domain! Quelle domage!

Look it up; λ = 10, k = 2 . N'est-ce pas?

-- Cheers, --M. d.