Answer the following: (A) Find the binomial probability P(x = 6), where n = 15 a

Question

Answer the following:
(A) Find the binomial probability P(x = 6), where n = 15 and p = 0.70.
(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate µ and s in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.


Assume that the population of heights of female college students is approximately normally distributed with mean m of 64.64 inches and standard deviation s of 6.02 inches. A random sample of 98 heights is obtained. Show all work.
(A) Find P (x > 63.75)
(B) Find the mean and standard error of the distribution
(C) Find P( line over x > 63.75)
(D) Why is the formula required to solve (A) different than (C)?

Explanation / Answer

(A) binompdf(15,0.70,6) = 0.0116 (B) binomcdf(15,0.70,6) = 0.0152 (C) nq = 15*0.3 = 4.5 < 5 so you shouldn't use the normal approximation, and even if you did, it only works for cumulative probabilities, not specific probabilities. (A) normalcdf(63.75,99999,64.64,6.02) = 0.5588 (B) I assume you mean of the sampling distribution of the sample means, in which case the mean is 64.64 and the SD is 6.02/sqrt(98) = 0.61 (C) normalcdf(63.75,99999,64.64,0.61) = 0.9283 (D) Because in (C) you're looking at the mean height of 98 people instead of the height of a single person.

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