Harper MTH165 Homework Section 6.2 Latest 2020 MAY

MTH165 ELEMENTARY STATISTICS

Homework Section 6.2

In this section you learned how many things in everyday life can be modeled with a normal distribution.

                All normal curves have two parameters:  _____ and __ ___

                The center of the curve is determined by the value of _  ___

                How wide the curve gets is determined by the value of ____ __

                What will happen to the graph of a normal curve if we increase the value of μ?

                What will happen to the graph of a normal curve if we increase the value of σ?

                The transition points (inflection points) are the places where the curve changes from a “hill” to a “valley”.  The distance from the mean to the transition point is ___, _______ _________________.

                The area under the whole curve is exactly ____.

                Fill in the 8 areas of the curve below with the correct 8 percentages for a normal curve.

Fill in the following as you work through your given problems in MyOpenMath.

 

1.            μ= _____ because _____mean is the on the axis at the center of the curve is the mean of a normal distribution.

                σ= ______ because ___ the distance from the mean to the transition point is 9

2.            μ= _____ because _____ mean is the on the axis at the center of the curve is the mean of a normal distribution._________________________________________________

                σ= ______ because ________ the distance from the mean to the transition point is 9________________________________________________

3.            Compare the means:____ The three distributions have different values for the mean___________________________________________________________

Explain your reasoning:________ because each curve has a different center;

Compare the standard deviations: the three distributions have the same standard deviation

Explain your reasoning:_________ because the distance from each graph’s mean to the transition point or inflection point is the same for each distribution___________________________________________________

4.            Compare the means:  ____ The three distributions all have the same mean___________________________________________________________

                Explain your reasoning:  _____ because each curve has the same center_______________________________________________________

                __________________________________________________________________________________

                Compare the standard deviations: ____ the three distributions have different standard deviations___________________________________________________

                Explain your reasoning:  ___ because the distance from each graph’s mean to the transition point or inflection point is different for each distribution_________________________________________________________

5.a.         Individual:  a randomly selected __dishwasher__________________________________

Variable:  _____________lifetime_______________________

Type of variable:  qualitative                       quantitative-discrete                     quantitative-continuous

b.            rv X = the _______ lifetime _________________________________________of a r.s. ___________ dishwasher ______

List the given values with their correct symbols:  μ ____ = __________                 __  ___ = ___________

c.             The Empirical Rule can be used because __ approximate probabilities for problems where the random variable has a normal distribution. It is given in the problem that the random variable has a normal distribution. ______________________________________________

Fill in the following with the correct 8 percentages and correct 7 values on the axis.

d.            P(  5.25< X ?<18.75               ) = ___________________________ = ___________

Interpret in the context of this problem:

_________________There is about 99.7% of dishwashers that last between 5.25 years and 18.75 years.________________________________________________________

e.            P(  X ?≥5.25                ) = __________0.15_________________ = __0.15%_________

6.a.         Individual:  ________________________________

Variable:  ____________ ________________________

Type of variable: 

b.rv X = the _____________ ___________________________________ of a r.s. ________ _________

List the given values with their correct symbols:  _ μ ___ = __________                                __ σ ___ = ___________

c.             The Empirical Rule can be used because __it is used to approximate probabilities for problems where the random variable has a normal distribution. It is given in the problem that the random variable has a normal distribution. ______________________________________________

Fill in the following with the correct 8 percentages and correct 7 values on the axis.

d.            P(      397<( X) ?<865            ) = ___________________________ = __________

Interpret in the context of this problem:

e.            P(    ( X) ?≥631              ) = ___________________________ = ___________