2) use the normal approximation to the binomial to find the probability for n=13

Question

2) use the normal approximation to the binomial to find the probability for n=13,p=0.5 and X 7. Round z-value calculations to 2 decimal places and final answers to 4 decimal places. The probability is ______

3)use the normal approximation to the binomial to find the probability for n=50,p=0.7 and X40. round z- value calculations to 2 decimal places and final answer to 4 decimal places. The probability is _____

4)For n=50 and p=0.8 check the binomial distribution to see whether it can be approximated by a normal distribution.

5) of all 3-to 5 year old children 56% are enrolled in school. if a sample of 500 such children is randomly selected find the probability that at least 264 will be enrolled in school. round the final answer to 4 decimal places and round intermediate z-value calculations to decimal to 2 decimal places

P(X 264)=_____

6) a mail order company has an 6 % success rate. if it mails advertisements to 594 people find the probability of getting less than 29 sales. Round z value calculations to 2 decimal places and final answers to 4 decimal places.

P(X<29)=_______

7)according to recent surveys 60% of households have personal computers. if a random sample of 177 households is selected what is the probability that more than 53 but fewer than 92 have a personal computer? round z-value calclations to 2 decimal places and final answer to 4 decimal places/

P(53<X<92)

Explanation / Answer

(2)

Given that

n=13,p=0.5 and X 7.

using the normal approximation to the binomial

mean (mu) = np=13 * 0.5=6.5

S.D ( sigma )=sqrt(13 *0.5 *0.5) =1.8028

so, p(x 7)

p(x > 6.5)

= p(z >(( 6.5-6.5) /1.8028)

= p(z > 0)

= 1- p(z< 0)

= 1- 0.5000

=0.5000

therefore, p(x > 6.5) = 0.5000

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