14 MCQs in Statistics ...

1. An investment project is expected to earn $100,000 on average with a standard deviation of $50,000. Assume earnings from this investment project is a normal distribution. Determine the probability that the annual net cash flow will be negative ( 0 or less earnings)

Answer: 0.50 

2.An investment project is expected to earn $100,000 on average with a standard deviation of $50,000. Assume earnings from this investment project is a normal distribution. What is the annual net cash flow at a probability of 75%. 

Answer: -$66275 or $133725

3.The two parameters used to describe normal distributions are: 

Answer: Mean (μ) and Standard deviation (σ)

4.The time at which the mailman delivers the mail follows a normal distribution with a mean of 2:00PM and a standard deviation of 15 minutes. What is the probability that the mail will arrive after 2:15PM? 

Answer: 0.1587

5.The breakdown voltage of a randomly chosen diode of a certain type is known to be normally distributed with a mean value 40 V and a standard deviation 1.5 V. What is the probability that a voltage of a single diode is between 39 and 42?

Answer: 0.6563 

6.The breakdown voltage of a randomly chosen diode of a certain type is known to be normally distributed with a mean value 40 V and a standard deviation 1.5 V. b) What is the probability that a voltage of a single diode will exceed 42?

Answer: 0.0912

7.The average life of a bread making machine is 7 years with a standard deviation of 1 year. Assume that the lives of these machines follow a normal distribution. What is the probability that the mean life of a random sample of 9 machines is less than 6.4 

Answer: 0.0359

8.The average life of a bread making machine is 7 years with a standard deviation of 1 year. Assume that the lives of these machines follow a normal distribution. What is the standard error for a random sample of 9 machines. 

Answer: 0.3333 year

9.What would the standard deviation have to be if the average is 100,000 and the probability that a random variable x is less than 109,000 is 80%. 

Answer: 10693.92

10.The probability that z is less than a Z value of 2.44 is: 

Answer: 0.9927

11.The standardized normal distribution is a normal distribution with the following characteristics

Answer: Mean = 0, Standard deviation = 1 

12.The standard error of the mean is: 

Answer: It is the standard deviation of the distribution of the sample mean over repeated samples. It is calculated by the 

formula SEM = s / √n, where s = sample standard deviation and n = sample size

13.For normal distribution problems, we use the transformation formula to calculate Z. The formula for Z is the x value subtracted by the mean divided by the variance. Is this true or false 

Answer: False 

14.What is the Z value for variable x equal to 10 and the mean is 20 with a standard deviation of 5 

Answer: -2