A mAth12 question?

Question

Eggs chosen a random are normally distributed with a mean length of 6 cm and a standard deviation of 0.3 cm.If the longest 9% of the eggs are classified as premium eggs, what is the length of the shorest premium egg?? the Ans is 6.4 but i dont know how to get this ans!?

but i still dont understant that how come the smallest eggs are longer than the mean, 6.0 cm. is it suppose to be smaller??

thnx for the ans!
thatsso cool!!! lol!!

Answer 1

Using your normal table, you find that the top 9% of a normally-distributed corresponds to a z-score of 1.341. Then use the mean and the SD to the desired value:

1.341 = (x - 6) / .3
.4023 = x - 6
6.4023 = x

Answer 2

u have to use the formula for normal distribution which is
z=(x- u)/Q where u is the mean, and Q being the standard deviation,( the formula is suppose to be Greek letters but i dont know how to input them),, to solve this problem you need standard normal probabilities table to obtain the z value for the bottom 91% since that is what you are looking for, so now you just plug in the values, on the table the bottom 91% corresponds to z=1.3 , so then 1.3=(x- 6)/(.3) and solve for X which is the shortest length of the premium egg,, so (1.3)(.3) + 6 = 6.39 so about 6.4 sorry this is my best explanation

Answer 3

this one's nasty.
by the way it can't be normally distibuted else you could expect to find some eggs with negative length but lets ignore that shall we.
The distribution is 1/(0.3sqrt2pi)exp(-((x-6)/0.3sqrt2)^2)
You need to integrate that from y to infinity and find out the value of y when the integral = 0.09.
erfc((y-6)/0.3sqrt2)=0.09
This can't be solved analytically so you look it up in a table and hopefully get 6.4

Answer 4

There are altogether 2^10 = 1024 approaches to respond to. a) there is in undemanding words a million thanks to get none maximum recommendations-blowing. So P0 = a million/1024. b) There are 10C3 approaches to get 3 maximum recommendations-blowing. So P3 = (10C3)/1024. c) there is in undemanding words a million thanks to get all maximum recommendations-blowing. So P10 = a million/1024. d) There are 10C5 approaches to get precisely 1/2 maximum recommendations-blowing. So P5 = (10C5)/1024.