stat 153

Question 1

1. The area under a normal curve is equal to 1 (100%).

1.       The area under any normal curve is equal to 1.  a. True 

b. False

 

True

False

0.25 points  

Question 2

1. The diameters of red delicious apples of an orchard have a normal distribution with a mean of 3 inches and a standard deviation of 0.5 inch. One apple will be randomly chosen. What is the probability of picking an apple with diameter less than 2.15 inches?

		-3.85
		0.9554
		0.0446
		-1.7

0.5 points  

Question 3

1. The diameters of red delicious apples of an orchard have a normal distribution with a mean of 3 inches and a standard deviation of 0.5 inch. One apple will be randomly chosen. What is the probability of picking an apple with diameter greater than 3.76 inches?

		1.52
		0.0643
		0.0125
		0.9357

0.5 points  

Question 4

1. The diameters of red delicious apples of an orchard have a normal distribution with a mean of 3 inches and a standard deviation of 0.5 inch. One apple will be randomly chosen. What is the probability of picking an apple with diameter between 2.5 and 4.25 inches?

		0.1649
		-0.8351
		0.8351
		1.5

1 points  

Question 5

1. The diameters of red delicious apples of an orchard have a normal distribution with a mean of 3 inches and a standard deviation of 0.5 inch. What diameter measurement separates the smallest 33%?

Round your answer to 2 decimal places.

1 points  

Question 6

1. As the sample size _____, the standard deviation of the population of all sample means decreases.

		decreases
		increases

0.25 points  

Question 7

1. The amount of time that it takes to complete a statistic exam has a skewed left distribution with a mean of 60 minutes and a standard deviation of 9 minutes. If 36 students are randomly sampled, determine the probability that the sample mean of the sampled students is less than 56 minutes.

		0.0038
		0.9962
		0.3300
		0.6700

1 points  

Question 8

1. The time until first failure of a brand of ink jet printers is normally distributed with a mean of 1500 hours and a standard deviation of 160 hours. A large company buys four such printers.  What is the probability that the mean lifetime of the four printers is more than 1568 hours? Round to 4 decimal places.

1 points  

Question 9

1. Based on past experience, a bank believes that 4% of the people who receive loans will not make payments on time. The bank has recently approved 300 loans.  6% of these clients did not make timely payments. 

What is p?  Blank 1

What is  ?  Blank 2

0.5 points  

Question 10

1. Based on past experience, a bank believes that 4% of the people who receive loans will not make payments on time. The bank has recently approved 300 loans.  6% of these clients did not make timely payments.  What is  ?  

Round your answer to 4 decimal places.

		0.0113
		0.0002
		0.0137
		0.0013

0.5 points  

Question 11

1. Based on past experience, a bank believes that 4% of the people who receive loans will not make payments on time. The bank has recently approved 300 loans.  6% of these clients did not make timely payments.  What is the probability that over 6% will not make timely payments?

		0.0721
		0.9616
		0.9279
		0.0384

0.75 points  

Question 12

1. Suppose the proportion of all college students who have used marijuana in the past 6 months is p = 0.40. In a class of 200 students that are representative of all college students, would it be unusual for the proportion who have used marijuana in the past 6 months to be less than 0.32?

		No, because the sample proportion is less than 2 standard deviations from the population proportion.
		Yes, because the sample proportion is less than 2 standard deviations from the population proportion.
		No, because the sample proportion is more than 2 standard deviations from the population proportion.
		Yes, because the sample proportion is more than 2 standard deviations from the population proportion.

Last week we studied probability, so this week's discussion has us reflecting on ways that people frequently misunderstand probability, specifically, the gambler's fallacy and the so-called "law of averages" which isn't a law at all!

You can find out what the gambler's fallacy and the supposed "Law of Averages " are by performing a quick google search.  The idea behind these FALSE beliefs (the "law of averages" is not a real law!) is that if you keep losing and losing and losing, at some point, your luck HAS to turn around and you have to win at some point.  

Let's imagine we are all in Vegas together, and we are playing Roulette or some game where each trial is independent of the next.  Explain WHY the supposed "law of averages" and the gambler's fallacy are false since each trial is independent from the next.  Write at least two paragraphs to explain your thoughts.  You may choose to do some background reading on this topic if you wish, but if you do please cite your sources.  

This is one of my favorite topics because to me it represents the intersection of psychology (the way people think is rarely rational!  Human beings are quite a superstitious lot!) and statistics.