[Blindmath] Statistics help

[Godfrey, Jonathan]

Two questions.

Neither uses the empirical rules; both use the standard normal tables.

P(116<X<120)
=P(X<120)-P(X<116)
=P(Z<(116-118.5)/1.2) - P(Z<(120-118.5)/1.2)
Sorry, no tables in this office. R used instead.
pnorm(120, 118.5, 1.2)
## [1] 0.8943502
pnorm(116,118.5,1.2)
## [1] 0.01861043
pnorm(120, 118.5, 1.2) - pnorm(116,118.5,1.2)
## [1] 0.8757398


The second question is worded in a very horrible way. For the purposes of this calculation, the mean and the point of interest are reversed, that is, assume the mean is 115 (temporarily) and look for the point that would have the requisite 12.1% above it.
Again, I used R:
qnorm(0.121, 115, 1.2, lower.tail=FALSE)
## [1] 116.40

I think the first question is fairly standard intro content, but the second is assuming a bit more knowledge of the ability to invert the problem and I wouldn't consider it reasonable to use in a test or exam.

Jonathan

-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Sabra Ewing via Blindmath
Sent: Wednesday, 21 September 2016 1:08 p.m.
To: blindmath at nfbnet.org
Cc: Sabra Ewing
Subject: [Blindmath] Statistics help

I need help with this statistics problem because I don't have access to many of the formulas  in my class. I tried to work with a group, but they haven't been very nice. They have just said that we went over it in class, when I can't understand what my professor writes on the board, and have received very little material in an accessible format. Anyways, here's the problem.

A large number of voltages show a mean of 118.5V and a population standard deviation of 1.20V. Determine the percentage of data that falls between 116 and 120 Volts. If it is desired to have 12.1% of the voltage below 115V, how should the mean voltage be adjusted? The dispersion is σ = 1.20 V.

I know it has something to do with the empirical rule, but I don't know what to do because it doesn't fall an even number of standard deviations from the mean. For the second part of the problem, I have no idea what to do.




          




Sabra Ewing
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