Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. How many are expected to attend their graduation?
e. Find the probability that 17 or 18 attend.
f. Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically
a. The random variable X is the number of students that attended their graduation.
b. The values that X may take on are
c. The distribution
d. are expected to attend the graduation.
e. The probability of attend is
f. Yes, it will be surprising if all attended graduation as it is unusual.
The binomial distribution determines the probability of looking at a specific quantity of a hit results in a specific quantity of trials.
We are given,
of graduating students attend their graduation and a group of graduating students is randomly chosen.
Random variable in simple terms generally refers to variables whose values are unknown, therefore, in this case the random variable X is the number of students that attended their graduation.
Make the list of values that you want to use X may take on.
As we can see there is an upper bound for the situation at hand , then X is given by
The random variable is distributed by the data provided X is the number of students that attended their graduation.
According to the given information, students attend their graduation.
The probability distribution of binomial distribution has two parameters and The binomial distribution is of the form:
Therefore, according to given information and
The distribution of X is
The expected binomial distribution is calculated as:
is average number of students attending graduation,
is number of trials
is probability of success.
The probability that attend is calculated as follow:
Using calculator we have found that if all students attends graduation which comes out to be:
, less than .
Therefore, it is unusual.
An instructor feels that 15% of students get below a C on their final exam. She decides to look at final exams (selected randomly and replaced in the pile after reading) until she finds one that shows a grade below a C. We want to know the probability that the instructor will have to examine at least ten exams until she finds one with a grade below a C. What is the probability question stated mathematically?
Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.
Find the standard deviation.
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