Ace Your Binomial Probability Tests with Plainmath's Expert Help and Detailed Resources

An agent sells life insurance policies to five equally aged, healthy people.
According to recent date, the probability that a person lives in these conditions for 30 years or more is ${\displaystyle \frac{3}{5}}$. Then the probability that after 30 years exactly two people are still living is:

Classify the following variables as continuous or discrete:
a.) A binomial distribution of the number of green pea plants in a batch of six ?
b.) The test scores of this final examination ?
c.) A binomial probability distribution of coin flips landing heads ?

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
${\displaystyle n=5,p=0.85,x=3}$
${\displaystyle P\left(3\right)=}$

Determine whether you can use the normal distribution to approximate the binomial distribution. If you​ can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you​ cannot, explain why and use the binomial distribution to find the indicated probabilities.
A survey of adults in a region found that 33​% name professional football as their favorite sport. You randomly select 11 adults in the region and ask them to name their favorite sport. Complete parts​ (a) through​ (d) below
​(a) Find the probability that the number who name professional football as their favorite sport is exactly 8.

Give the numerical value of the parameter p in the following binomial distribution scenario.
The probability of winning an arcade game is 0.632 and the probability of losing is 0.368. If you play the arcade game 10 times, we want to know the probability of winning no more than 8 times.
Consider winning as a success in the binomial distribution. Do not include ${\displaystyle p=}$ in your answer.

According to a 2014 Gallup poll. 56% of uninsured Americans who plan to get health insurance say they will do so through a government health insurance exchange.
a) What is the probability that in a random sample of 10 people exactly 6 plan to get health insurance through a goverment health insurance exchange?
b) What is the probability that in a random sample of 1000 people exactly 600 plan to get health insurance through a government health insurance exchange?
c) What are the expected value and the variance of X?
d) What is the probability that less than 600 people plan to get health insurance through a government health insurance exchange?

To find: The probability of getting exactly 14 variegated plants.
Given info:
A nursery provides red impatiens for commercial landscaping. If 5% are variegated instead of red. A sample of 200 plants was taken.

Suppose ${\displaystyle X\sim B(n=10,p=.3)}$ using the binomial distribution table we have: ${\displaystyle P\left(X<4\right)}$ is:
a) .3828
b) .8497
c) .4059
d) .6496

A coin is tossed n times.
a) What is the probability that exactly k heads occur?
b) What is the probability that at most two heads occur?
Type in your answers below in terms of k and n. As a student of computer science, your typeset answer should be an accurate use of the characters (parentheses, slash, exponent symbol, etc).

A binomial probability is given. Write the probability in words.​ Then, use a continuity correction to convert the binomial probability to a normal distribution probability.
${\displaystyle P(x=114)}$
Write the probability in words.
The probability of getting ? 114 successes.
Which of the following is the normal probability statement that corresponds to the binomial probability statement?
A) ${\displaystyle P\left(113.5<x<114.5\right)}$
B) ${\displaystyle P\left(x<114.5\right)}$
C) ${\displaystyle P\left(x<113.5\right)}$
D) ${\displaystyle P\left(x>114.5\right)}$
E) ${\displaystyle P\left(x>113.5\right)}$

Find the value of ${\displaystyle P(X=7)}$ if X is a binomial random variable with ${\displaystyle n=8}$ and ${\displaystyle p=0.9}$.

X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
${\displaystyle P(7<X\le 10)}$

Assume that a procedure yields a binomial distribution with ${\displaystyle n=6}$ trials and a probability of success of ${\displaystyle p=0.50}$. Use a binomial probability table to find the probability that the number of successes x is exactly 3.
Click on the icon to view the binomial probabilities table.
${\displaystyle P\left(3\right)=0.257}$ (Round to three decimal places as needed.)

A retailer is receiving a large shipment of media players. In order to determine whether she should accept or reject the shipment, she tests a sample of media players; if she finds at least one defective player, she will reject the entire shipment. If 0.5% of the media players are defective, what is the probability that she will reject the shipment if
a)she tests fifteen media players.
b)she tests thirty media players.

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. ${\displaystyle P(X=14),n=16,p=0.8}$

Assume that a procedure yields a binomial distribution with a trial repeated ${\displaystyle n=13}$ times. Use either the binomial probability formula (or technology) to find the probability of ${\displaystyle k=12}$ successes given the probability ${\displaystyle p=83\mathrm{\%}}$ of success on a single trial.
(Report answer accurate to 4 decimal places.)

80% A poll is given, showing are in favor of a new building project. 8 people are chosen at random, what is the probability that exactly 3 of them favor the new building project?

Whether it is surprising for more than 4 elk in the sample to survive to adulthood and calculate an appropriate probability.
Given information:
Number of trials, ${\displaystyle n=7}$
Probability of success, ${\displaystyle p=44\mathrm{\%}=0.44}$

a. To List: The mid-point values for the binomial probability.
b. The binomial probability of getting between 57 and 83 successes in a normal distribution probability by using a continuity correction.

To write: The binomial probability ${\displaystyle P(x\le 36)}$ in words.
To convert: The binomial probability to a normal distribution probability by using continuity correction.