Statistics- normal distribution

Question

$6000$ eggs in a large store have masses which are normally distributed. The mean mass of the eggs are $42$ grams with a standard deviation of $5.5$ grams.

1) $4000$ of the $6000$ eggs have masses greater than W grams. Estimate the value of $W$ correct to one decimal place??

Thanks in advance - I can't solve it

$39.6$ is answer in book

Yes I have tried the formula for Z score : z = x-mean all over standard deviation — user112639, Dec 01 '13 at 13:28
Stephencormac
New Member
Join Date Dec 2013 Posts 5 Z= 0.43 for the area 0.6666

0.43 = x-42 / 5.5 Which works out as x = 44.4. i can't get 39.6 though — user112639, Dec 01 '13 at 14:12
@user112639: You should be able to figure this out if you understand the normal density curve and how the area under it relates to the probability diagrammatically. Did you understand why you want to calculate the area under the curve of the Normal variate? — Sauvik De, Dec 01 '13 at 16:41

score 0 · Answer 1 · answered Dec 02 '13 at 14:31

I was able to get 39.6 using just the CDF of a normal distribution:

What you want to find is $W:P(X\leq W) = 1-\frac{4000}{6000} \approx 0.33$

For a standard normal, $\Phi(-0.43073) \approx 0.33$ you can get this from NORM.INV in Excel. Now, it is a simple matter to transform the standard normal to your situation:

$W=42+5.5(-0.43073) = 39.6$

Statistics- normal distribution

1 Answers1