Harper MTH085 Week 7 Worksheet Chapter 6

MTH085                                                                           Chapter 6 Worksheet

 

1. Consider an exam where the mean score was 85 pts, the standard deviation was 5 pts and the distribution of all scores was normal.

 

Individual: a r.s._________________________

 

Variable: ____________________________________

 

rv X = the ___________________ of a randomly selected ______________________

X has a ______________ distribution with parameters         = _____               = ______

 

a.   Find the percentage of scores that would fall between 82 points and 88 pts on the exam.

 

 

 

P(                 ) = ________________________________________ = __________

 

probability statement        expression typed on calculator                               answer to 4 decimal places

 

b.   Find the percentage of scores that would fall below 88 pts on the exam.

 

 

P(                 ) = ________________________________________ = __________

 

probability statement        expression typed on calculator                                answer to 4 decimal places

 

c.   Find the percentage of scores that would fall above 90 pts on the exam.

 

 

P(                 ) = ________________________________________ = __________

 

probability statement        expression typed on calculator                                 answer to 4 decimal places

 

1. Find an estimate for the probability above using the Empirical Rule.

 

 

 

 

 

 

 

 

1. Find an estimate for the percentage of scores that would fall below 70 points on the exam.

 

 

1. Find an estimate for the percentage of scores that would fall between 80 and 95 points on the exam.

 

 

1. In c) we saw that using the typical 90-80-70-60 cutoffs for A-B-C-D that about 15.9% of the class would have gotten As. Let’s say that the scores on that exam are going to be curved such that only 10% of the class receive As on the exam. What score separates the As from the Bs in this case?

 

Designate on the graph below where the given percentage should go and then compute.

 

 

 

_________________________________ = __________ _________

 

expression typed on calculator                    answer                units

 

1. If the curve is set such that the middle 50% of the scores receive Cs, for what interval of scores will students receive a grade of C?

 

 

_________________________________ = __________ _________

 

 

expression typed on calculator                    answer                units

 

MTH085                                                                           Chapter 6 Worksheet

 

 

1. A company claims that their light bulbs have a mean lifetime of 750 hours with a standard deviation of 10.6 hours. Assume the lifetimes have a normal distribution.

 

rv X = the ___________________ of a randomly selected ______________________

X has a ______________ distribution with parameters         = _____               = ______

 

1. What proportion of light bulbs have a lifetime less than 725 hours? Probability inequality: TI83/84 input:

 

Correctly rounded answer (4 dec pl):

 

1. Would it be unusual to have one of these light bulbs last less than 725 hours?

 

Since _______________________________, 725 hours (is/is not) an unusually short lifetime.

 

1. About how many light bulbs out of 100,000 would you expect to have lifetimes less than 725 hr?

 

 

 

1. Is 765 hours an unusually long lifetime for one of these light bulbs? Why or why not? Probability inequality:

 

TI83/84 input:

 

Correctly rounded answer (4 dec pl):

Since _______________________________, 765 hours (is/is not) an unusually long lifetime.

 

1. If the company wants to provide a warranty, how many hours should they guarantee that the bulbs will last such that no more than 2% will fail before then?

 

 

Probability inequality:

 

TI83/84 input:

 

Correctly rounded answer (1 dec pl):

 

They should guarantee that one of these light bulbs will last at least ___________ hours.

f.   What are the quartiles of the distribution of lifetimes?