Question

A survey of U.S. adults found that 69% of those who text on cell phones receive spam or unwanted messages. You randomly select 100 U.S. adults who text on cell phones and ask who receive spam or unwanted messages. A) Write a complete sentence in the context of the problem that describes what p represents in this problem. No numbers. B) Are the criteria for using the normal distribution met? EXPLAIN. Show any necessary calculations. C) If many samples of size 100 each are taken, sketch the ?̂sampling distribution. Label the mean and label two standard deviations in both directions on the sketch. D) Find the probability that in a random sample of 100 U.S. adults you would get a sample where less than 60% have received spam or unwanted messages? (1) Mark this value on the sketch above and shade the area in question. (2) Show your work and provide your final answer as a sentence in the context of the problem.

Answer 1

A) In this problem, p is the proportion of U.S. adults who have received spam or unwanted messages.

B) Given and .

Since and are both greater than 5, the criteria for using the normal distribution met.

C) The Mean and standard deviation are:

D) The probability that in a random sample of 100 U.S. adults you would get a sample where less than 60% have received spam or unwanted messages is:

1)

2) The probability that in a random sample of 100 U.S. adults you would get a sample where less than 60% have received spam or unwanted messages is 0.0256.