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.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)