Abinomial 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 45% 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.

a) no, because np< 5.
b) no because nq< 5
c) yes, the mean is and the standard deviation is

Yes, The mean is 18 and the standard deviation is approximately 3.146.

Step-by-step explanation:

Consider the provided information.

A survey of adults found that 45% 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.

n = 40, p = 45% = 0.45, and  q = 1 – 0.45 = 0.55

If np ≥ 5 and np ≥ 5, then the binomial random variable, x is approximately normally distributed, then Mean µ = np and standard deviation σ =, where n is the sample size, p is the population proportion, and q = 1 – p.

Now calculate np and nq.

np = (40)(0.45) = 18

nq = (40)(0.55) = 22

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

Thus, µ = np

µ = 40(0.45)=18

Standard deviation,

.

Therefore, the mean is 18 and the standard deviation is approximately 3.146.

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