Questions
Probability is the link between Descriptive Statistics and Inferential Statistics. So get out your dice, coins,...

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

The following data describe a clinical trial of an allergy medication: Allergy Drug Placebo Control Total...

The following data describe a clinical trial of an allergy medication:
Allergy Drug Placebo Control Total
Improvement 65 42 31 138
No Improvement 55 58 49 162
Total 120 100 80 300
a. What is the probability that a randomly selected person in the study was given either the drug or the placebo?
b. What is the probability that a randomly selected person either improved or did not improve?
c. What is the probability that a randomly selected person either was given the drug or improved?
d. What is the probability that a randomly selected person was given the drug and improved?

In: Statistics and Probability

Recently, birth weights of Norwegians were reported to have a mean of 3668 grams and a...

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...

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)...

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...

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...

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...

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...

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....

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