12-5 CW - 5.5

The sample size n, probability of success p, and probability of failure q are given for a binomial experiment. Decide whether you can use the normal distribution to approximate the random variable x.

n = 19 p = 0.77 q = 0.23

• Yes, because np ≥ 5 and nq ≥ 5

• No, because nq < 5.

• No, because np < 5 and nq < 5

• No, because np < 5

Tags

CCSS.HSS.ID.A.4

The sample size n, probability of success p, and probability of failure q are given for a binomial experiment. Decide whether you can use the normal distribution to approximate the random variable x.

n = 20 p = 0.36 q = 0.64

• No, because np < 5 and nq < 5.

• Yes, because np ≥ 5 and nq ≥ 5.

• No, because nq < 5.

• No, because np < 5

Tags

CCSS.HSS.ID.A.4

Use the correction for continuity and determine the normal probability statement that corresponds to the binomial probability statement.

Binomial Probability P(x < 110)

Which of the following is the normal probability statement that corresponds to the binomial probability statement?

• P(x > 110.5)

• P(x > 109.5)

• P(x < 109.5)

• P(x < 110.5)

A binomial probability is given. Write the probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability.

 $P\ \left(x\ \le62\right)$  
Which of the following is the normal probability statement that corresponds to the binomial probability statement?

•  $P\left(x<62.5\right)$  

•  $P\left(x<61.5\right)$  

•  $P\left(x\le62.5\right)$  

•  $P\left(x\le61.5\right)$  

A binomial probability is given. Write the probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability.

P(x = 134)

Write the probability in words. The probability of getting (1) _____________134 successes.

• at most

• fewer than

• exactly

• more than

• at least

A binomial probability is given. Write the probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability.

P(x = 24)

Which of the following is the normal probability statement that corresponds to the binomial probability statement?

• $P\left(23.5<x<24.5\right)$

• $P\left(23.5>x>24.5\right)$

• $P\left(x>23.5\right)$

• $P\left(x<24.5\right)$

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 65% have used a multivitamin in the past 12 months. You randomly select 50 adults and ask them if they have used a multivitamin in the past 12 months.

• No, because nq < 5.

• No, because np < 5.

• Yes, the mean is 32.5 and the standard deviation is 3.37 (Round to two decimal places as needed.)

• Yes, the mean is 7.37 and the standard deviation is 3.27 . (Round to two decimal places as needed.)

Tags

CCSS.HSS.ID.A.4

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 teenagers found that 89% have a cell phone. You randomly select 18 teenagers and ask them whether they have a cell phone.

• Yes, the mean 16.02 is and the standard deviation is 1.33. (Round to two decimal places as needed.)

• No, because nq < 5

• No, because np < 5.

• Yes, the mean 1.98 is and the standard deviation is 1.03. (Round to two decimal places as needed.)

Tags

CCSS.HSS.ID.A.4

Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities.

A survey of adults found that 69% of those who text on cell phones receive spam or unwanted messages. You randomly select 100 adults who text on cell phones.

• No, because nq < 5

• No, because np < 5.

• Yes, because both np ≥ 5 and nq ≥ 5.

• Yes, because both np < 5 and nq < 5.

A survey of adults found that 69% of those who text on cell phones receive spam or unwanted messages. You randomly select 100 adults who text on cell phones.

Find the probability that the number of people who receive spam or unwanted messages is exactly 72. (Round the mean and standard deviation into two decimal places as needed.)

• 0.007

• 0.071

• 0.064

• 0.034

Tags

CCSS.HSS.ID.A.4