Quiz chapter 6

Question 1

Explain continuous distributions

Answer 1

Continuous distributions are constructed from continuous random variables in which values are taken on for every point over a given interval and usually are generated from experiments in which things are “measured” as opposed to “counted”.

Question 2

Explain a uniform distribution

Answer 2

A relatively simple continuous distribution in which the same height, or f(x), is obtained over a range of values.

Question 3

How do you find the height of a uniform distribution?

Answer 3

• 1/b-a is the height

Question 4

Explain discrete random variables

Answer 4

Discrete random variables – the probability mass function f (x) provides the probability that the random variable assumes a particular value.

Question 5

Explain continuous random variables

Answer 5

• Continuous random variables – the counterpart of the probability mass function is the probability density function, also denoted by f (x).
• The probability density function does not directly provide probabilities.
• We are computing the probability that the random variable assumes any
  value in an interval.
• For continuous random variables, the probability of any particular value of the random variable is zero.

Question 6

What is the area under a continuous distribution?

Answer 6

1

Question 7

What are the normal distribution characteristics?

Answer 7

• It is a continuous distribution
• It is a symmetrical distribution about its mean (The highest point on the normal curve is at the mean, which is also the median and mode of the distribution)
• It is asymptotic to the horizontal axis
• It is unimodal
• It is a family of curves The entire family of normal distributions is differentiated by two parameters: the mean
  and the standard deviation
• Area under the curve is 1

Question 8

The normal distribution is described by what?

Answer 8

The normal distribution is described by its mean and standard deviation

Question 9

All normal distributions can be converted into a single what?

Answer 9

to a single distribution, the z distribution, using the formula:

A z score is the number of standard deviations that a value, x, is above or below the mean

The z distribution is a normal distribution with a mean of 0 and a standard deviation of 1

Question 10

Explain z distributions

Answer 10

• The z distribution probability values are given in the standard normal table
• Since the normal distribution is symmetric, the area under the curve is the same whether z is positive or negative, so only positive values of z are listed in the table
• The table areas (probabilities) are always positive

Question 11

When the sample size is large what occurs?

Answer 11

When the sample size is large, the binomial distribution approaches the normal distribution in shape regardless of the value of p

Question 12

Using the Normal Curve to Approximate
Binomial Distribution Problems

Answer 12

• For large n values, it is cumbersome to use the binomial formula, and tables usually go only to an n value of 25
• As a rule of thumb, the normal approximation is good enough if both n∙p > 5 and n∙q > 5
• Since a discrete distribution is being approximated by a continuous distribution, it is necessary to add a correction for continuity

Question 13

Explain Exponential distributions

Answer 13

Exponential distribution: continuous and describes a probability distribution of the times between random occurrences
* It is a continuous
distribution
* It is a family of distributions
* It is skewed to the right
* The x values range from zero to infinity
* Itsapexisalwaysatx=0
* The curve steadily decreases as x gets larger