Question

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 41 ​% 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.

Answer 1

GIVEN:

Number of adults (or trials)

Probability of adults who used a multivitamin in the past 12 months

SOLUTION:

The condition to be satisfied for the normal approximation to binomial distribution is:

• 
• 

Let us first check these two conditions:

Thus the conditions and are satisfied. We can use normal approximation to binomial distribution.

MEAN:

The mean is given by,

  

STANDARD DEVIATION:

The standard deviation is given by,

  

The normal approximation can be used. The mean is and the standard deviation is .