Question

In: Statistics and Probability

A telephone exchange operator assumes that 7% of the phone calls are wrong numbers. Step 1...

A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.

Step 1 of 1:

If the operator is right, what is the probability that the proportion of wrong numbers in a sample of 487 phone calls would differ from the population proportion by more than 3% ? Round your answer to four decimal places.

Solutions

Expert Solution

Solution:

Given that,

n = 487

= 7% =0.07

1 - = 1 - 0.07 = 093

= = 0.07

= $\sqrt$ ( 1 - ) / n

= $\sqrt$ 0.07 * 0.93 / 487

= 0.0116

P( > 0.03 )

1 - P ( 0.04 < < 0.10 )

1 -P ( 0.04 - 0.07 / 0.0116 ) < ( - / ) < ( 0.10 - 0.07 / 0.0116 )

1 -P ( - 0.03 / 0.0116 < z < 0.03 / 0.0116 )

1 - P (-2.59 < z < 2.59 )

1 - P ( z < 2.59) - p ( z < -2.59 )

Using z table

= 1 - ( 0.9952 - 0.0048)

= 1 - 0.9904

= 0.0096

Probability = 0.0096

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A telephone exchange operator assumes that 7% of the phone calls are wrong numbers. If the...

A telephone exchange operator assumes that 7% of the phone calls are wrong numbers. If the operator is right, what is the probability that the proportion of wrong numbers in a sample of 487 phone calls would differ from the population proportion by more than 3%? Round your answer to four decimal places.

A telephone company claims the average number of phone calls made every day in a household...

A telephone company claims the average number of phone calls made every day in a household is more than three. A random sample of 169 days is survey in a mean of two and a standard deviation of .2 are found, test the claim at a 5% level of significance. Assume the district distribution is normal.

telephone calls arrive at an exchange have a poisson distribution at an average rate of one...

telephone calls arrive at an exchange have a poisson distribution at an average rate of one every second. Find the probabilities of the following; a. no calls arriving in a given five-second period b. between four and six calls arriving in the five-second period c. there is atleast one call d. there is at most one call

7 During the period of time that a local university takes phone-in registrations, calls come in...

7 During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes. What is the probability of receiving NO calls in a 10-minute period? What is the probability of receiving more than five calls in a 10-minute period? What is the probability of receiving less than seven calls in 15-minutes? What is the probability of receiving at least three but no more than 10 calls in 12 minutes?...

7) Personal phone calls received in the last three days by a new employee were 4,...

7) Personal phone calls received in the last three days by a new employee were 4, 1, and 8. Assume that samples of size 2 are randomly selected with replacement from this population of three values. a) List the nine different possible samples of size 2 and find the mean of each of them. b) The probability for each sample mean in Part a) is 1/9. Summarize your results in Part a) by construct ing a sampling distribution for these...

How many 7-digit telephone numbers are possible if the first digit cannot be eight and (a)...

How many 7-digit telephone numbers are possible if the first digit cannot be eight and (a) only even digits may be used? (b) the number must be a multiple of 10 (that is, it must end in 0)? (c) the number must be a multiple of 1,000? (d) the first 2 digits are 92? (e) no repetitions are allowed?

You will write a program that prompts the user to enter a 7-digit phone numbers, and...

You will write a program that prompts the user to enter a 7-digit phone numbers, and finds the 3- and 4-letter words that map to the phone number, according to the restrictions outlined earlier. A sample run: unixlab% java MapNumbers Enter name of dictionary file: words10683 Enter a test word (3 letters): cat Test word maps to 228 Enter telephone number (7 digits, no 0's or 1's, negative to quit): 2282273 Options for first 3 digits: act cat bat Options...

Part 1: A particular telephone number is used to receive both voice calls and fax messages....

Part 1: A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 6 of the calls involve a fax message? (b) What is the probability that exactly 6 of the calls involve a fax message? (c) What is the probability that at least...

1.)In a mid-size company, the distribution of the number of phone calls answered each day by...

1.)In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 51 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 43 and 59? 2.)A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of...

1. An agency is having problems with personal phone calls made during working hours. Each minute...

1. An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.25 in wasted wages. The agency decides to hire operators to monitor calls in order to attain the optimal number of personal calls (minimize total cost of personal calls). Number of Operators Total minutes of personal calls (per hour) 0 1130 1 980 2 855 3 740 4 635 5 540 6 460 a. What is the...

Subjects