Question

1/ Consider the following table. Defects in batch Probability 2 0.18 3 0.29 4 0.18 5 0.14 6 0.11 7 0.10 Find the standard deviation of this variable. 1.52 4.01 1.58 2.49

2/ 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? Supplier B, 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 A, 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

3/ A survey found that 39% of all gamers play video games on their smartphones. Ten frequent gamers are randomly selected. The random variable represents the number of frequent games who play video games on their smartphones. What is the value of p? 10 0.10 x, the counter 0.39

4/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. (1) 0.753 (2) 0.256 (1) 0.247 (2) 0.256 (1) 0.247 (2) 0.744 (1) 0.753 (2) 0.744

5/Say a business found that 29.5% of customers in Washington prefer grey suits. The company chooses 8 customers in Washington and asks them if they prefer grey suits. What assumption must be made for this study to follow the probabilities of a binomial experiment? That the probability of being a selected customer is the same for all 8 people That there is a 29.3% probability of being a selected customer That those selected have similar characteristics to those in the original study That the probability of preferring grey suites is the same as preferring suits of other colors

6/ Eight baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 93.8% of all their baseballs have straight stitching. If exactly six of the eight have straight stitching, should the company stop the production line? No, the probability of exactly six have straight stitching is not unusual No, the probability of six or more having straight stitching is not unusual Yes, the probability of exactly six having straight stitching is unusual Yes, the probability of six or more having straight stitching is unusual

7/A soup company puts 20 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 24 cans has all cans that are properly filled? n=20, p=0.97, x=20 n=24, p=0.97, x=24 n=24, p=0.97, x=1 n=20, p=0.97, x=20

8/A supplier must create metal rods that are 2.1 inches width to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are too wide, too narrow, or about right? No, as there are three possible outcomes, rather than two possible outcomes Yes, all production line quality questions are answered with binomial experiments No, as the probability of being about right could be different for each rod selected Yes, as each rod measured would have two outcomes: too long or too short

9/In a box of 12 pens, there is one that does not work. Employees take pens as needed. The pens are not returned, once taken. You are the 5th employee to take a pen. Is this a binomial experiment? No, the probability of getting the broken pen changes as there is no replacement No, binomial does not include systematic selection such as “fifth” Yes, you are finding the probability of exactly 5 not being broken Yes, the probability of success is one out of 12 with 5 selected

10/Fifty-three percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual? 0, 1, 2, 8 1, 2, 7, 8 1, 2, 8 0, 1, 7, 8

11/Eighty-one percent of products come off the line within product specifications. Your quality control department selects 15 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired? Fewer than 9 Fewer than 10 Fewer than 11 Fewer than 12

12/The probability of a potential employee passing a drug test is 91%. If you selected 15 potential employees and gave them a drug test, how many would you expect to pass the test? 13 employees 15 employees 14 employees 12 employees

13/The probability of a potential employee passing a training course is 86%. If you selected 15 potential employees and gave them the training course, what is the probability that more than 11 will pass the test? 0.648 0.352 0.900 0.852

14/ Off the production line, there is a 4.6% chance that a candle is defective. If the company selected 50 candles off the line, what is the standard deviation of the number of defective candles in the group? 1.10 2.19 1.48 2.30

Please, i am indeed need help with these questions. Thank you.

Answer 1

Consider the following table:

x	P(x)	x P(x)	x²P(x)
2	0.18	0.36	0.72
3	0.29	0.87	2.61
4	0.18	0.72	2.88
5	0.14	0.70	3.50
6	0.11	0.66	3.96
7	0.10	0.70	4.90
Sum	1.00	4.01	18.57

The standard deviation is:

$\sigma=\sqrt{\sum x^2 P(x)-\left [\sum xP(x) \right ]^2}=\sqrt{18.57-(4.01)^2}={\color{Red} 1.58}$