Answered

Find expert answers and community-driven knowledge on IDNLearn.com. Join our platform to receive prompt and accurate responses from experienced professionals in various fields.

A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard
deviation. If you cannot, explain why.
A survey of adults found that 66% have used a multivitamin in the past 12 months. You randomly select 40 adults and ask them if they have used a multivitamin in the
past 12 months.
Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
OA. No, because np < 5.
B. No, because nq <5.
OC. Yes, the mean is_______
(Round to two decimal places as needed.)
and the standard deviation is _____

A Binomial Experiment Is Given Decide Whether You Can Use The Normal Distribution To Approximate The Binomial Distribution If You Can Find The Mean And Standard class=

Sagot :

Yes, the mean is 26.4 and the standard deviation is 3

How to find the mean in binomial experiment?

We are given;

n = 40, p = 66% = 0.66, and  q = 1 – 0.66 = 0.34

If np ≥ 5 and np ≥ 5, then the binomial random variable, x is approximately normally distributed, then;

Mean; µ = np

Standard deviation; σ = √npq

where;

n is the sample size.

p is the population proportion.

q = 1 – p.

Calculating np and nq gives;

np = (40)(0.66) = 26.4

nq = (40)(0.34) = 13.6

Both np and nq are greater than 5, the normal distribution can be used to approximate the binomial distribution.

Thus, µ = np

µ = 40(0.66) = 26.4

Standard deviation;

σ = √(40 * 0.66 * 0.34)

σ = 3

Read more about Binomial Experiment at; https://brainly.com/question/9325204

#SPJ1

We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.