Question

Question

Consider the following table.

Defects in batch	Probability
2	0.35
3	0.23
4	0.20
5	0.09
6	0.07
7	0.06

Find the standard deviation of this variable.

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

Group of answer choices

3.48

4.50

1.51

2.27

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Question

The standard deviation of samples from supplier A is 0.0841, while the standard deviation of samples from supplier B is 0.0926. Which supplier would you be likely to choose based on these data and why?

Homework Help:

3DD. Interpreting and comparing discrete variable standard deviations (Links to an external site.) (DOCX)

Group of answer choices

Supplier A, as their standard deviation is higher and, thus easier to fit into our production line

Supplier B, as their standard deviation is lower and, thus, easier to fit into our production line

Supplier B, as their standard deviation is higher and, thus, easier to fit into our production line

Supplier A, as their standard deviation is lower and, thus, easier to fit into our production line

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Question

Fifteen golfers are randomly selected. The random variable represents the number of golfers who only play on the weekends. For this to be a binomial experiment, what assumption needs to be made?

Homework Help:

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments (Links to an external site.) (DOCX)

Group of answer choices

The probability of being selected is the same for all fifteen golfers

All fifteen golfers play during the week

The probability of golfing on the weekend is the same for all golfers

The probability of golfing during the week is the same for all golfers

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Question

A survey found that 31% of all teens buy soda (pop) at least once each week. Seven teens are randomly selected. The random variable represents the number of teens who buy soda (pop) at least once each week. What is the value of n?

Homework Help:

3DE. Definitions, assumptions and elements (n, x, p) of binomial experiments (Links to an external site.) (DOCX)

Group of answer choices

0.07

0.31

x, the counter

7

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Question

Sixty-eight percent of US adults have little confidence in their cars. You randomly select eleven US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly eight and then find the probability that it is (2) more than 6.

Homework Help:

3VB. Calculating binomial probabilities and cumulative probabilities (Links to an external site.) (8:23)

3DF. Binomial probabilities versus cumulative probabilities (Links to an external site.) (DOCX)

Group of answer choices

(1) 0.753 (2) 0.256

(1) 0.753 (2) 0.744

(1) 0.247 (2) 0.256

(1) 0.247 (2) 0.744

Answer 1

Solution-:

For Q. (1)

For this question we prepare following table:

Defects in batch (xi)	Prob. (pi)	pi*xi	pi*xi^2
2	0.35	0.7	1.4
3	0.23	0.69	2.07
4	0.2	0.8	3.2
5	0.09	0.45	2.25
6	0.07	0.42	2.52
7	0.06	0.42	2.94
Total	1	3.48	14.38

and

  

  

  

Option (3) 1.51 is correct.

Q. (2) Option (4) Supplier A, as their standard deviation is lower and, thus, easier to fit into our production line is correct.

Because, the minimum standard deviation said that the variation in data are less.

Q. (3) Let, X=the number of golfers who only play on the weekends.   n=15

For this to be a binomial experiment, assumption needs to be made,

Option (3) The probability of golfing on the weekend is the same for all golfers is corect

Q.(4) Let, X=the number of teens who buy soda (pop) at least once each week.

Here,

This situatuation is suitable for binomial distribution with parameter and

Option (4) 7 is corrcct.

Q.5 Let, X= Number of US adults have little confidence in their cars among 11 US adults.

Here,

This situatuation is suitable for binomial distribution with parameter and

The p.m.f. of X is given by,

             

We prepare the following table for finding probabilities:

	n=11	p=0.68	q=0.32
x	nCx	p^x	q^(11-x)	P[X=x]
0	1	1	0.000	0.000
1	11	0.68	0.000	0.000
2	55	0.4624	0.000	0.001
3	165	0.314432	0.000	0.006
4	330	0.213814	0.000	0.024
5	462	0.145393	0.001	0.072
6	462	0.098867	0.003	0.153
7	330	0.06723	0.010	0.233
8	165	0.045716	0.033	0.247
9	55	0.031087	0.102	0.175
10	11	0.021139	0.320	0.074
11	1	0.014375	1.000	0.014

(i) P[the number of US adults who have little confidence in their cars is exactly eight]

The required probability is 0.247

(ii) P[ the number of US adults who have little confidence in their cars is more than 6]

The required probability is 0.744

Therfore, Option (4) (1) 0.247 (2) 0.744 is correct