An instructor asked a random sample of eight students to record their study times at the beginning of a course. she then made a table for total hours studied? (x) over 2 weeks and test score? (y) at the end of the 2 weeks. the table is given below-

x 9 17 10 19 7 16 12 22
y 96 82 80 72 89 76 85 75
\sumx= 112 \sum y=655 \sum xy=8935 \sum x2 = 1764

compute? sst, ssr, and? sse, using the? formulas,

sstequals=summation from nothing to nothing y subscript i superscript 2 baseline minus left parenthesis summation from nothing to nothing y subscript i right parenthesis squared divided by n? y2i? ? yi2/n? ,

ssrequals=startfraction left parenthesis summation from nothing to nothing x subscript i baseline y subscript i baseline minus left parenthesis summation from nothing to nothing x subscript i baseline right parenthesis left parenthesis summation from nothing to nothing y subscript i baseline right parenthesis divided by n right parenthesis squared over summation from nothing to nothing x subscript i superscript 2 baseline minus left parenthesis summation from nothing to nothing x subscript i baseline right parenthesis squared divided by n endfraction? xiyi? ? xi? yi/n2? x2i? ? xi2/n? ,

and

sseequals=sstminus? ssr.

1. sst= ? round to two decimal places as? needed.)

2. ssr= ? round to two decimal places as? needed.)

3. sse= ? round to two decimal places as? needed.)

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Ответ:

terriblexsiren

18.09.2020

Mathematics

a) W is a binomial random variable because in each trial there are only two possible outcomes, and the probability of a success is always the same.

b) 0.2013 = 20.13% probability that you win exactly 3 times.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

a. Explain why W is a binomial random variable.

For each time a duck is selected, there are only two possible outcomes. Either it has a star, or it does not. Also, after a duck is selected, it is placed back in the water which means that in each trial, the probability of finding a duck with star is the same. This is why W is a binomial random variable.

b. Find the probability that you win exactly 3 times.

Let W=the number of times you win if you play this game 10 times.

This means that n = 10

The game claims to have 20 ducks with stars among the 100 ducks.

This means that $p = \frac{20}{100} = 0.2$

We have to find P(X = 3). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013$

0.2013 = 20.13% probability that you win exactly 3 times.

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