What are the mean and standard deviation of a binomial probability distribution with #n=11 # and #p=7/30 #?

Answer 1

Mean is #2.567# and Standard Deviation is #1.403#

For a binomial probability distribution with #n=11# and #p=7/30#
Mean is given by #np=11xx7/30=2.567#
Standard Deviation is given by #sqrt(npq)# where #q=1-p#
Hence, Standard Deviation is #sqrt(11xx7/30xx(1-7/30))#
= #sqrt(11xx7/30xx23/30#
= #(sqrt(11xx7xx23))/30# = #1.403#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

The mean (( \mu )) of a binomial distribution is calculated using the formula ( \mu = np ), where ( n ) is the number of trials and ( p ) is the probability of success in each trial.

Given ( n = 11 ) and ( p = \frac{7}{30} ), we have: [ \mu = 11 \times \frac{7}{30} = \frac{77}{30} ]

The standard deviation (( \sigma )) of a binomial distribution is calculated using the formula ( \sigma = \sqrt{np(1-p)} ).

Substituting the given values: [ \sigma = \sqrt{11 \times \frac{7}{30} \times \left(1 - \frac{7}{30}\right)} ] [ \sigma = \sqrt{11 \times \frac{7}{30} \times \frac{23}{30}} ] [ \sigma = \sqrt{\frac{161}{150}} ]

Therefore, the mean (( \mu )) is ( \frac{77}{30} ) and the standard deviation (( \sigma )) is ( \sqrt{\frac{161}{150}} ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7