What four conditions must be met to use a binomial distribution?

The four conditions are: a fixed number of trials each trial has two possible outcomes the trials are independent the probability of success stays constant

Why might a binomial distribution NOT be suitable for a snowboarder's repeated attempts at a trick?

The trials may not be independent, because she could get better with practice. For the same reason the probability of success may not stay constant, and both of those are conditions the binomial needs.

True or False? In a binomial distribution, a 'success' has to be a good thing.

False. 'Success' is simply the name given to one of the two outcomes being counted. Counting the number of faulty items in a batch is a perfectly ordinary binomial situation.

True or False? In a normal distribution the mean, the median and the mode are all the same value.

True. The curve is symmetrical and bell-shaped about its centre, so all three averages sit at that same central point.

What happens to a normal curve if the standard deviation increases but the mean stays the same?

The curve is stretched out horizontally, becoming shorter and wider. A small standard deviation gives a tall narrow curve instead, with the data clustered closely around the mean.

What three conditions must hold for a normal distribution to be a suitable model?

The data must be continuous , the distribution must be symmetrical and bell-shaped, and the mean, median and mode must be approximately equal. That rules out skewed data, where those three averages are not close together.

GCSEStatisticsEdexcelHigherFlashcardsProbabilityProbability Distributions

Probability Distributions (Edexcel GCSE Statistics: Higher): Flashcards

Exam code: 1ST0

1/15

0Still learning

Know0

FrontThe Binomial Distribution
What four conditions must be met to use a binomial distribution?
BackThe Binomial Distribution
The four conditions are:
a fixed number of trials
each trial has two possible outcomes
the trials are independent
the probability of success stays constant
BackThe Binomial Distribution
Sign up to unlock flashcards
Join for free to unlock a full flashcard set, track what you know,
and turn revision into real progress.

Was this flashcard helpful?

Cards in this collection (15)

What four conditions must be met to use a binomial distribution?
The four conditions are:
- a fixed number of trials
- each trial has two possible outcomes
- the trials are independent
- the probability of success stays constant
What do the two numbers in $B (n, p)$ stand for?
$n$ is the number of trials and $p$ is the probability of success on each one.
The probability of failure is then $q = 1 - p$ for that same trial.
Hannah attempts a snowboard trick 12 times and succeeds 20% of the time. Write down her binomial distribution.
It is $B (12, 0.2)$ for the number of successful attempts.
Writing the probability as $\frac{1}{5}$ instead would be equally correct.
Why might a binomial distribution NOT be suitable for a snowboarder's repeated attempts at a trick?
The trials may not be independent, because she could get better with practice.
For the same reason the probability of success may not stay constant, and both of those are conditions the binomial needs.
True or False?
In a binomial distribution, a 'success' has to be a good thing.
False.
'Success' is simply the name given to one of the two outcomes being counted.
Counting the number of faulty items in a batch is a perfectly ordinary binomial situation.
What is the mean of a binomial distribution, and what does it tell you?
The mean of $B (n, p)$ is $n p$ for that distribution.
It is the expected number of successes in $n$ trials.
Complete the formula for the probability of $r$ successes, filling in the two missing powers.
$P (r successes) = (n C r) p^{______} q^{______}$
The completed formula is:
$P (r successes) = (n C r) p^{r} q^{n - r}$
For $B (4, 0.4)$ find the probability of getting exactly 3 successes.
With $4 C 3 = 4$ from the calculator, substitute into the formula.
$4 \times 0 . 4^{3} \times 0 . 6^{1} = 0.1536$
How can Pascal's triangle help with binomial probabilities?
Each row gives the numbers in front of the powers when ${(p + q)}^{n}$ is expanded.
The row reading 1, 4, 6, 4, 1 is the $n = 4$ row, matching the five possible numbers of successes in four trials.
True or False?
In a normal distribution the mean, the median and the mode are all the same value.
True.
The curve is symmetrical and bell-shaped about its centre, so all three averages sit at that same central point.
Complete the notation for a normal distribution.
$N (______,______)$
The completed notation is:
$N (μ, σ^{2})$
The first parameter is the mean and the second is the variance, which is the standard deviation squared.
What happens to a normal curve if the standard deviation increases but the mean stays the same?
The curve is stretched out horizontally, becoming shorter and wider.
A small standard deviation gives a tall narrow curve instead, with the data clustered closely around the mean.
What three conditions must hold for a normal distribution to be a suitable model?
The data must be continuous, the distribution must be symmetrical and bell-shaped, and the mean, median and mode must be approximately equal.
That rules out skewed data, where those three averages are not close together.
Complete the three percentages for a normal distribution.
About $______$ per cent of the data lies within one standard deviation of the mean, about $______$ per cent within two standard deviations, and about $______$ per cent within three.
The completed percentages are:
About 68 per cent of the data lies within one standard deviation of the mean, about 95 per cent within two standard deviations, and about 99.7 per cent within three.
Boys' heights have a mean of 175.8 cm and a standard deviation of 6.4 cm. What percentage are taller than 163.0 cm?
163.0 cm is two standard deviations below the mean, and 47.5% of the data lies between there and the mean.
Adding the 50% that lies above the mean gives $47.5 + 50 = 97.5$ per cent.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:Probability Basics