still having difficulty after reading previous threads

[klewis]

Regarding Question #2

[U][Second Question/U]

In grading apples into "A","B" and "C" a large orchard uses weights to distinguish apples. Any apple weighing more than 2 ounces is classified as Grade "A" while apple weighing less than 0.75 ounces is classified as Grade "C". If the days pick shows 16.6% are Grade "A" and 6.68% are Grade C, determine the mean and standard deviation. Assume weights are normally distributed.

Here is a HINT that I dont get - First calculate the appropriate z values for the probabilities given, then set up your equations to solve for the mean and standard deviation

=====> I understand that x=2.0 and x=.75 .....I have been taught to draw a symmetric curve to solve for x and z values, but never taught how to solve for u (mean) and s (standard deviation)
the formula I have been taught to use is z= x - u / s ===> or x=u-(s*z)
I will admit my algebra is not good, been a while

Also, that half of the curve is .5 and other half is .5
P(o<z) = P(z<o) and usually add or subtract .5 accordingly

thus z value for 2.0 is 100-16.6 = .834 - .5 is .334 (z value on chart is 0.97)
and z value for 0.75 is 100-6.68 =.9332 - .5 is .4332 (z value on chart is 1.5)
is there an easier way than this to find z chart value??

I used the formulas that you suggested for Shannon

u = x - (z*s)

but I don't understand how she arrived at s = 1.78

and how to calculate for u after getting value for s

[JohnM]

If you keep reading the post you'll see that I corrected her. She should have gotten z values of 0.97 for x=2 and -1.50 for x=0.75.

Using u = x - (z * s) both both sets, you'll get two equations with two unknowns:

u = 2 - (0.97 * s)
u = 0.75 - (-1.5 * s)

solve for s, you get s = 0.506

plug it back into any of the two equations:

u = 2 - (0.97 * 0.506) = 1.509

[klewis]

u=2-(0.97*s) I get 1.03
u=0.75 -(-1.5*s) I get 2.25

1.03+2.25 =3.28/2 = 1.65

still not getting s=.506

please bear with me as I am struggling with solving for mean and standard deviation as I have not encountered any examples thus far in my self study text book

P.S. I know that usually you only help members solve equations on their own but I really need to understand the entire equation process (formula) so I can replicate and understand how to arrive at the answer on my own

[JohnM]

u = 2 - (0.97 * s)
u = 0.75 - (-1.5 * s)

set the right-hand sides equal to each other, since they're both equal to u:
2 - (0.97 * s) = 0.75 - (-1.5 * s)
2 - 0.97s = 0.75 + 1.5s
2 - 0.75 = 1.5s + 0.97s
1.25 = 2.47s
1.25/2.47 = s
0.506 = s

Plug s=0.506 into either of the original equations:
u = 2 - (0.97s)
u = 2 - (0.97*0.506)
u = 2 - (.491)
u = 1.509

[klewis]

it is my algebra that is weak and now I can understand what I did wrong, I truly appreciate your quick response as I become consumed by a question when I cannot figure it out myself!!