Statistic hw?

1. Top 15% of student get A.Sample 4 from 200 to complete problem. That 2 of 4 got A%26#039;s use:

A. Binomial distribution

B.normal distribution

C.T dis 3 degree of freedom

d. T distribution with 199 deg.

E. None

2. Summary measure computed from population is a ?

A.Parameter

b.Stats

c. population

d.Sample

e. None

3. Sampled 20 banks and recorded rates for 30 years.Data is

A.discrete

B.continuous

c. binomial

d. none

Statistic hw?quick loan

1) the answer is A, binomial. It can%26#039;t be any of the others, the normal and the student t are both continuous distribution, but the question asked deals with discrete probabilities. So that means only A could be correct. Why is this binomial? The binomial is the sum of n independent and identically distributed Bernoulli trials. In this case each Bernoulli trial is one of the four students sampled. Each as a 15% probability of having an A.

Let X be the number of students sampled who have an A. X has the binomial distribution with n = 4 trials and success probability p = 0.15

In general, if X has the binomial distribution with n trials and a success probability of p then

P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)

for values of x = 0, 1, 2, ..., n

P[X = x] = 0 for any other value of x.

The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.

Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.

X ~ Binomial( n , p )

the mean of the binomial distribution is n * p = 0.6

the variance of the binomial distribution is n * p * (1 - p) = 0.51

the standard deviation is the square root of the variance = 鈭?( n * p * (1 - p)) = 0.7141428

The Probability Mass Function, PMF,

f(X) = P(X = x) is:

P( X = 0 ) = 0.5220062

P( X = 1 ) = 0.368475

P( X = 2 ) = 0.0975375

P( X = 3 ) = 0.011475

P( X = 4 ) = 0.00050625

2) parameter.

parameters define populaitons, statistics are from samples.

3) the data is continuous because the rates could be any value between 0 and 100%.