Math Is Fun Forum

kendraap

Member

Registered: 2015-09-29

Posts: 1

Statistics--HELP

Hello,

I have a couple of questions I need some assistance in.  If anyone can please help me get started with this I appreciate it:

1.  Heights of women have a bell-shaped distribution with a mean of 165cm and a standard deviation of 5cm.  Using Chebyshev's theorem, what do we know about the percentage of women with heights that are within 2 standard deviations of the mean?  What are the minimum and maximum heights that are within 2 standard deviations of the mean?

At least ___% of women have heights within 2 standard deviations of 165cm?  (Round to the nearest percent as needed)
The minimum heights that is within 2 standard deviations of the mean is ___cm
The maximum height that is within 2 standard deviations of the mean is ___cm

2.  Ted is not particularly creative.  He uses the pickup line " If I could rearrange the alphabet.  I'd put U and I together".  The random variable x is the number of girls Ted approaches before encountering one who reacts positively.  Determine whether the table describes a probability distribution.  If it does, find its mean and standard deviation.
x      P(x)
1      0.002
2      0.026
3      0.119
4      0.265
5      0.234

Find the mean of the random variable.  Select the correct choice below and, if necessary.  Fill in the answer box to complete your choice.
a-
b- the table is not a probability distribution

Find the standard deviation of the random variable x.  Select the correct choice below and if necessary fill in the answer box to complete your choice.
a-
b- the table is not a probability distribution

Thank you everyone for your assistance.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Statistics--HELP

Okay, I'll take a stab at 1 before somebody who actually knows tells ya. I could very well be wrong but I believe 2 standard deviations is defined as 95% are within mean. Since they gave you one standard deviation, I would guess that min height is 155cm and max is 175cm. Annnnnd BOY, could I be wrong. Haha!!

Last edited by Newman (2015-09-29 09:25:29)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Statistics--HELP

hi kendraap

Welcome to the forum.

I would have used 2 standard deviations too, but, I thought I'd better look up Chebyshev's theorem.

https://en.wikipedia.org/wiki/Chebyshev%27s_inequality

In practical usage, in contrast to the 68-95-99.7% rule, which applies to normal distributions, under Chebyshev's inequality a minimum of just 75% of values must lie within two standard deviations of the mean and 89% within three standard deviations.

question 2:  "Determine whether the table describes a probability distribution.  "  Have you been given a method for doing this ?

LATER EDIT:  I had assumed the question wanted you to identify the distribution (eg. binomial)  and I couldn't see how you could do that with any certainty.  If you don't find a 'fit' that doesn't mean that one doesn't exist and if you find a distribution that is 'close' that doesn't mean it is right.

But, re-reading the question, I wonder if this is just about the fact that the probabilities don't add up to 1.  Are you just expected to say it cannot be a probability distribution because of this.  It seems a bit simple but maybe that is all this question is about.

Bob

Last edited by Bob (2015-09-30 06:49:04)

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob