Question

Binomial experiments are listed. Decide whether you can use the normal distribution to approximate x with a normal distribution. If you can, find the mean and standard deviation. If you cannot, explain why (or show your work to why not). Part A Five percent of adults in the United States are planning to purchase a 3D television in the next two years. You randomly select 125 adults in the United States and ask them if they are planning to purchase a 3D television in the next two years. ​ Part B A survey of US adults found that 15% read every work of a contract for buying or selling a home before signing. You randomly select 25 adults and ask them if they read every word when buying or selling a home before signing.

Answer 1

Answer: Part A Five percent of adults in the United States are planning to purchase a 3D television in the next two years. You randomly select 125 adults in the United States and ask them if they are planning to purchase a 3D television in the next two years.

Solution:

p = 5% = 0.05

n = 125

mean = np

= 125 x 0.05

= 6.25

Standard deviation = √npq

= √125*0.05*0.95

= 2.4367

Therefore,

Yes. Normal approximation can be used because, n is fixed, sample is random and independent, np > 5.

Answer Part B A survey of US adults found that 15% read every work of a contract for buying or selling a home before signing. You randomly select 25 adults and ask them if they read every word when buying or selling a home before signing.

Solution:

p = 15% = 0.15

n = 25

mean = np

= 25 * 0.15

= 3.75

Standard deviation = √npq

= √25 * 0.15 * 0.85

= 1.7854

Therefore,

No, Normal approximation cannot be used because, n is fixed, sample is random and independent, np < 5.