Probability Help: Margarine Production & Electric Toasters

[cattmiow]

Hi Everyone,
Trying to make my way through bunch of problems and have run into drama with 2 questions. Any help would be great!

The daily production of a margarine process is known to follow a normal distribution with a mean of 410 tons per day and a variance of 144 tons per day.
Find the probability that the days production will be between 388 and 427 tons.

I used normal distribution to find the prob that less than 427 tons are produced and substracted the prob that less than 388 tons are produced, however my answer doesn't match up with the back of the book...Do I need to convert to percentages??

A manufacturer knows that, on average, 2.2% of the electric toasters that she makes will require repairs within 90 days after they are sold. Use the normal approximation to the binomial distribution to determine the probability that among 2500 of these toasters at least (greater than or equal to) 59 will require repairs within the first 90 days after they are sold.
First I put n = 2500
p = 0.02
q= 1-p = 0.98
mu=n*p=50
standard dev=7
However where do I go from there??

Thanks so much to anyone that will help!

 

[CompuChip]

Hi Everyone,
Trying to make my way through bunch of problems and have run into drama with 2 questions. Any help would be great!

The daily production of a margarine process is known to follow a normal distribution with a mean of 410 tons per day and a variance of 144 tons per day.
Find the probability that the days production will be between 388 and 427 tons.

I used normal distribution to find the prob that less than 427 tons are produced and substracted the prob that less than 388 tons are produced

That sounds right.

however my answer doesn't match up with the back of the book...Do I need to convert to percentages??

Without telling us what you got and what it should be according to "the book", that would be hard to tell :)

However where do I go from there??

You calculate the probability. Don't forget to adjust the upper limit (I don't know its exact name, I usually call it "continuum correction") because the distribution is actually discrete.