A moving target at a police academy target range can be hit 78% of the time by a particular individual. Suppose that as part of a training exercise, she has to take eight shots at a moving target. a) What characteristics of this scenario indicate that you are working with Bernoulli trials? b) What is the probability that she hits the 4th target? c) What is the probability that the first time she hits a target is not until her fourth shot? Consider the question: What is the probability that she will hit 5 of the targets? Notice that this question is talking about any 5 of the targets and that there are many scenarios in which this could happen. Thus we should apply the binomial model to answer this question. There are two built-in commands for the binomial model in your graphing calculator, binompdf and binomcdf and they can be found by going to 2nd DISTR and choose option A or B. Use one of these commands to answer the questions (d) through (h) below. d) What is the probability that she will hit 5 targets? e) What is the probability that she will hit at most 6 targets? f) What is the probability that she will hit at least 4 targets? g) What is the probability that she will hit between 4 and 7 targets (inclusive)? h) What is the probability that she will hit at least one target? i) What is the mean and standard deviation of the number of targets hit?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
-
A moving target at a police academy target
range can be hit 78% of the time by a particular individual. Suppose that as part of a training exercise, she has to take eight shots at a moving target.
a) What characteristics of this scenario indicate that you are working with Bernoulli trials?
b) What is the
c) What is the probability that the first time she hits a target is not until her fourth shot?
Consider the question: What is the probability that she will hit 5 of the targets? Notice that this question is talking about any 5 of the targets and that there are many scenarios in which this could happen. Thus we should apply the binomial model to answer this question. There are two built-in commands for the binomial model in your graphing calculator, binompdf and binomcdf and they can be found by going to 2nd DISTR and choose option A or B. Use one of these commands to answer the questions (d) through (h) below.
-
d) What is the probability that she will hit 5 targets?
-
e) What is the probability that she will hit at most 6 targets?
-
f) What is the probability that she will hit at least 4 targets?
-
g) What is the probability that she will hit between 4 and 7 targets (inclusive)?
-
h) What is the probability that she will hit at least one target?
-
i) What is the mean and standard deviation of the number of targets hit?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
