Statistics and Probability Answers

A population has a mean of 200 and a standard deviation of 50 . A simple random sample of suze 100 will be taken and the sample mean will be use to estimate the population mean. The expected value of X is
1. 200
2. 100
3. 5
4. 20
5.150

Consider that Z is a standard normal distribution variable P(Z <- 1.57) is
1. 0.0668
2. 0.9418
3. 0.0582
4. 0.0401
5. -0.0582

A random variable is normally distributed with a mean of u=50 and a standard deviation of a=5 .The probability that the random variable will assume a value greater than 40 is
1. 0.9772
2. 0.0228
3. 0.4207
4. 0.5793
5. 0.4920

Consider a poison distribution with a mean ¡=3 then P( X<2) is
1. 0.2240
2. 0.1992
3. 0.4232
4. 0.1494
5. 0.4223

For sample of 11 units production employee during the most recent days
30 16 17 18 15 19 21 25 31 33 41
Which one of the following statement is incorrect?
1. The position of Q1=3
2. The value of Q2 =19
3. The media is 21
4. The value of Q3 is 31
5. The interquartile range is 14

A safety engineer feels that 35% of all industrial accidents in her plant are caused by failure of employees to follow instructions. She decides to look at the accident reports (selected randomly with replacement) until she finds one that shows an accident caused by failure of employees to follow instructions.

(i) On average, how many reports would the safety engineer expect to look at until she finds a report showing an accident caused by employee failure to follow instructions? (Enter your answer rounded to 4 decimal places)

(ii) What is the probability that the safety engineer will find the first report showing an accident caused by employee failure to follow instructions within the first 3 examined reports? (Enter your answer rounded to 4 decimal places)

A safety engineer feels that 35% of all industrial accidents in her plant are caused by failure of employees to follow instructions. She decides to look at the accident reports (selected randomly with replacement) until she finds one that shows an accident caused by failure of employees to follow instructions.

(i) On average, how many reports would the safety engineer expect to look at until she finds a report showing an accident caused by employee failure to follow instructions? (Enter your answer rounded to 4 decimal places)

(ii) What is the probability that the safety engineer will find the first report showing an accident caused by employee failure to follow instructions within the first 3 examined reports? (Enter your answer rounded to 4 decimal places)

A research firm conducted a survey to determine the mean amount of money smokers spend on cigarettes during a day. A sample of 100 smokers revealed that the sample mean is N$ 5.24 and sample standard deviation is N$ 2.18 Assume that the sample was drawn from a normal population. 2.5) Use the data provided above to test a claim at a 1 % Level of Significance that the unknown population mean of spending amount on cigarettes is N$ 5.00 (8)

Faculty salaries for a random sample of teachers in the public-school system of a certain town were
coded by dividing each salary by 1000. Find the MAD and standard deviation of these salaries if the
coded observations are 18, 15, 21, 19, 13, 15, 14, 23, 18, and 16 pesos.