PROBLEM SOLVING. Solve the problems in the or- der they are presented. Show comp

Question

PROBLEM SOLVING. Solve the problems in the or- der they are presented. Show complete work and clearly indicate all final answers. Round-olf final answers to Lwo decimal places. probability that A. 25 clients will use the ATM for any given hour? B. at least 2 will use the ATM for any given hour? 1. A survey of 50 students at Tarpon Springs College 3. A random sample of 150 reality show aspirants from the current season has a mean age of 25.72 years. Based on past seasons of the reality show, the population stan- dard deviation is assumed to be 12 years. Develop a 99% confidence interval for the population mean age of the reality show aspirants, assuming normal popu- lation. about the number of extracurricular activities resulted in the data shown ctivities 20 12 4. A survey of 611 office workers investigated telephoue answering practices, including how often each office worker was able to answer incoming telephone calls went directly to voice mail. A total of 281 office work- ers indicated that they never need voice mail and are able to take every telephone call. A. What is the probability that a student participates B. Let A be the event that a student participates in C. Let B be the event that a student participates in 3 2. A bank manager has observed that for every hour, an in exactly 2 activities? at most 2 activities. What is the P(A)? or more activities. Find P(B). A. What is the point estimate of the proportion of the population of office workers who are able to take every telephone call? B. What is the 90% confidence interval for the propor- tion of the population of office workers who are able to take every telephone call. average of 20 clients use the bank's ATM. What is the Good Luck!

Explanation / Answer

Question 1

Data and required probabilities are summarised in the following table:

No. Of Activities (X)

Frequency

P(X)

0

8

0.16

1

20

0.4

2

12

0.24

3

6

0.12

4

3

0.06

5

1

0.02

Total

50

1

Part A

Here, we have to find the probability that a student participates in exactly 2 activities.

P(X=2) = 12/50 = 0.24

Required probability = 0.24

Part B

Here, we have to find P(A) = P(X2)

P(X2) = P(X=0) + P(X=1) + P(X=2)

P(X2) = 0.16 + 0.40 + 0.24 = 0.80

Required probability = 0.80

Part C

P(B) = P(X3)

P(X3) = 1 - P(X2)

P(X3) = 1 – 0.80 = 0.20

Required probability = 0.20

Question 2

Here, we have to use Poisson distribution for calculating required probabilities.

P(X=x) = xe- /x!

We are given

= 20

Part A

We have to find P(X=25)

P(X=25) = 20^25*exp(-20)/25!

P(X=25) =0.044588

Required probability = 0.044588

Part B

Here, we have to find P(X2)

P(X2) = 1 – P(X1)

P(X1) = P(X=0) + P(X=1)

P(X=0) = 20^0*exp(-20)/0!

P(X=0) = 0.0000

P(X=1) = 20^1*exp(-20)/1!

P(X=1) = 0.0000

P(X1) = P(X=0) + P(X=1)

P(X1) = 0.0000

P(X2) = 1 – P(X1)

P(X2) = 1 – 0.0000

P(X2) = 1.0000

Required probability = 1.0000

No. Of Activities (X)

Frequency

P(X)

0

8

0.16

1

20

0.4

2

12

0.24

3

6

0.12

4

3

0.06

5

1

0.02

Total

50

1

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