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How do I know which distribution to use for the following and when/where do tables apply?:

Nonstandard Normal
Binomial
Normal
Standard normal
Central limit theorem

a) Mean is 0, stand. dev. is 0 degrees C., find P between 0.05 and 1.50
b)Mean is 63.6 and s.d. is 2.5; Club had requirement that women must be 70 inches tall-what % meets that?
c)Find the P35 separating top 35 from bottom 65% with mean = 143 and sd. of 29
d) Mean = 143, sd = 13; if 1 woamn randomly selected, find P weight between 143 and 150
e) If 100 women randomly selected, find P they have a mean weight greater than 140 pounds.

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Solution Summary

The solution discusses which distribution to use for the following and when/where do tables apply:

Nonstandard Normal
Binomial
Normal
Standard normal
Central limit theorem

a) Mean is 0, stand. dev. is 0 degrees C., find P between 0.05 and 1.50
b)Mean is 63.6 and s.d. is 2.5; Club had requirement that women must be 70 inches tall-what % meets that?
c)Find the P35 separating top 35 from bottom 65% with mean = 143 and sd. of 29
d) Mean = 143, sd = 13; if 1 woamn randomly selected, find P weight between 143 and 150
e) If 100 women randomly selected, find P they have a mean weight greater than 140 pounds.

Solution Preview

Nonstandard Normal: This type of distribution is applicable specifically when the sample size is small and the you are given that the data are not Guassian/Normal distributed. i.e.,
P(mu - sigma < x < mu+sigma) =! 68%
or
P(mu - 2sigma < x < mu + 2 sigma) =! 95%
Also the distribution may have some skewness.

Binomial distribution is used when the probability of an event is ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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