Probability is the link between Descriptive Statistics and Inferential Statistics. So get out your dice, coins, and cards. To get started, what is the probability of getting either a king or a red card if I pick a card at random from a standard deck of cards?
Also, let's say that a pro basketball player is a career 80% free throw shooter. Suppose the player attempts 4 free throws in a game. What is the probability that the player will make 2 of these 4 shots? As a first cut, do you think that the probability will be high or low?
In: Statistics and Probability
In: Statistics and Probability
Recently, birth weights of Norwegians were reported to have a
mean of 3668 grams and a standard deviation of 511 grams (g).
Suppose that a Norweigan baby was chosen at random.
(a) Find the probability that the baby’s birth weight was less than
4000 g.
(b) Find the probability that the baby’s birth weight was greater
than 3750 g.
(c) Find the probability that the baby’s birth weight was between
3000 g and 4000 g.
(d) Find the probability that the baby’s birth weight was less than
2650 g or greater than 4650 g.
In: Statistics and Probability
The population mean and standard deviation are given below. Find the indicated probability and determine whether a sample mean in the given range below would be considered unusual. If convenient, use technology to find the probability.
For a sample of
nequals=3131,
find the probability of a sample mean being less than
12 comma 74912,749
or greater than
12 comma 75212,752
when
muμequals=12 comma 74912,749
and
sigmaσequals=1.51.5.
For the given sample, the probability of a sample mean being less than
12 comma 74912,749
or greater than
12 comma 75212,752
is
nothing.
In: Statistics and Probability
Let X1 and X2 be a random sample from a population having
probability mass function f(x=0) = 1/3 and f(x=1) = 2/3; the
support is x=0,1.
a) Find the probability mass function of the sample mean. Note that
this is also called the sampling distribution of the mean.
b) Find the probability mass function of the sample median. Note
that this is also called the sampling distribution of the
median.
c) Find the probability mass function of the sample geometric mean.
Note that this is also called the sampling distribution of the
geometric mean.
In: Statistics and Probability
A committee of 2 women and 6 men is to be chosen randomly from a group of 18 women and 13 men.
a) What is the probability that "Ann" (female) and her friend "Bob" (male) are on the committee together?
b) What is the probability that ``Ann''(female) and her friend ``Bob''(male) are on the committee and their friends ``Carla''(female) and ``Dan''(male) are also on the committee?
c) Given that ``Carla'' and ``Dan'' have been chosen to be on the committee, what is the probability that ``Ann'' and her friend ``Bob'' are chosen to be on committee?
d) What is the probability that none of ``Ann'',``Bob'',``Carla'', or ``Dan'' are chosen to be on the committee?
In: Statistics and Probability
Suppose systolic blood pressure of 16-year-old females is
approximately normally distributed with a mean of 118 mmHg and a
variance of 421.07 mmHg. If a random sample of 16 girls were
selected from the population, find the following
probabilities:
a) The mean systolic blood pressure will be below
119 mmHg.
probability =
b) The mean systolic blood pressure will be above
124 mmHg.
probability =
c) The mean systolic blood pressure will be
between 112 and 120 mmHg.
probability =
d) The mean systolic blood pressure will be
between 107 and 113 mmHg.
probability =
In: Statistics and Probability
To reduce laboratory costs, water samples from twotwo public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past results, there is a 0.0040.004 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from twotwo public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely necessary?
The probability of a positive test result is (Round to three decimal places as needed.)
In: Statistics and Probability
| We have a system that has 2 independent components. Both
components must function in order for the system to function. The
first component has 9 independent elements that each work with
probability 0.91. If at least 6 of the elements are working then
the first component will function. The second component has 4
independent elements that work with probability 0.86. If at least 2
of the elements are working then the second component will
function. |
| (a) | [3 marks] What is the probability that the system functions? |
| (b) | [2 marks] Suppose the system is not functioning. Given that information, what is the probability that the second component is not functioning? |
In: Statistics and Probability
74. IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. X ~ _____(_____,_____) Find the probability that the person has an IQ greater than 120. Include a sketch of the graph, and write a probability statement. MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. Sketch the graph, and write the probability statement. The middle 50% of IQs fall between what two values? Sketch the graph and write the probability statement.
In: Statistics and Probability