Construct a frequency distribution table for the following:

1. Thirty-six customers were categorized according to civil status. The data set is

|Single |Single |Married |Married |Single |
|Single |18 |18 |0.5 |50 |
|Married |13 |13 |0.36 |36.1 |
|Widow |5 |5 |0.14 |13.9 |
|TOTAL |36 |36 |1 |100 |

2. Samples of forty-two (42) college students are considered for study and were categorized according to year level. The date set is

|Freshman |Freshman |Freshman |Sophomore |Junior |
|Freshman |15 |15 |0.36 |35.7 |
|Sophomore |12 |12 |0.29 |28.6 |
|Junior |9 |9 |0.21 |21.4 |
|Senior |6 |6 |0.14 |14.3 |
|TOTAL |42 |42 |1 |100 |

3. A sales representative for a publishing company recorded the following numbers of client contacts for 36 days that he was on the road in the month of May. Use the given data to construct a grouped frequency distribution. Determine the class boundaries, relative frequency, cumulative frequency, and midpoints. (Use Rule1/Formula 2-1)

|15 |17 |19 |20 |
|94-97 |3 |95.5 |3 |
|98-101 |8 |99.5 |11 |
|102-105 |12 |103.5 |23 |
|106-109 |10 |107.5 |33 |
|110-113 |6 |111.5 |39 |
|114-117 |1 |115.5 |40 |

a. Histogram

1. Consider the sample 7, 9, 10, 8, 20, 18, 19, 16, and 13. Find the mean.

Solutions:

2. Twelve randomly selected business administration students were asked to state the number of hours they slept last Sunday. The resulting data are 6, 7, 8, 10, 5, 4, 11, 12, 11, 10, 8, and 7. Find the mean.

Solutions:

3. A recent study showed that the cost of buying a typical “shopping basket” of 40 food items for consumption at home was P6,500 in Makati, P4,300 in Manila, P5,700 in Mandaluyong, P4,800 in Pasay, P5,600 in San Juan, and P4,100 in Pasig. Determine the mean of these data.

Solutions:

4. In a certain shopping mall, restaurants charge P125, P150, P200, P165, P175, P190, P230 and P180 for a regular dinner. Find the average cost.

Solutions:

5. Complete the table to find the mean for the grouped frequency distribution.

Solutions:

|Class Limits |f |X |fX |
|1-5 |3 |3 |9 |
|6-10 |4 |8 |32 |
|11-15 |5 |13 |65 |
|16-20 |8 |18 |144 |
|21-25 |2 |23 |46 |
|26-30 |1 |28 |28 |

N = 23

fX = 324

x = 93

6. Complete the table to find the mean for the grouped frequency distribution.

Solutions:

|Class Limits |f |X |fX |
|37-39 |3 |38 |114 |
|40-42 |6 |41 |246 |
|43-45 |10 |44 |440 |
|46-48 |5 |47 |235 |
|49-51 |4 |50 |200 |
|52-54 |2 |51 |102 |
|55-57 |1 |56 |56 |

N = 31

fX = 1,393

x = 327

7. Complete the table to find the mean for the grouped frequency distribution.

Solutions:

|Class Limits |f |X |fX |
|10-13 |4 |11.5 |46 |
|14-17 |7 |15.5 |108.5 |
|18-21 |8 |19.5 |156 |
|22-25 |13 |23.5 |305.5 |
|26-29 |3 |27.5 |82.5 |
|30-33 |2 |31.5 |63 |

N = 37

fX =76’

Solve the ff:

1. The daily income of bank auditors in SSS. Commercial bank is distributed with a mean of P675 and standard deviation of P50. What is the z value for the income X of a bank auditor who earns P750 daily? For an auditor who earns P550 daily?

Solutions:

2. The length of time needed for a service a motorcycle at ETS service station is normally distributed with mean of 6.5 minutes and standard deviation of 1.5 minutes. What is the probability that a randomly selected motorcycle will require more than 7 minutes of service or less than 5.5 minutes of service?

Solutions:

3. Monthly food expenditures for families in Caloocan City average P4, 250 with a standard deviation of P800. Assuming that the monthly food expenditures are normally distributed. What percentages of these expenditures are between P3, 322 and P5, 874?

Solutions:

Section Exercise 8.5

1. A report LTO stated that the average age of taxis in the Philippines is 9 years. An operational manager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is 8.2 years. The o of the population is 2.3 years. At a = 0.05, can it be concluded that the average age of the taxis in his company is less than the national average?

Solutions:

Step 1: state the hypothesis

Ho: The average age of the taxis in his company is not less than the national average.

Ha: The average age of the taxis in his company is less than the national average.

Step 2: The level of significance and critical region. A = ____ and Zcritical = ___

Step 3: Compute for the value of one sample z test. Zcomputed = _________.

Step 4: Decision rule

______________________________________________________

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Step 5: Conclusion

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2. Average college cost of tuition fee for all private institutions last year was P36, 400. A random sample of costs this year for 45 institutions of higher learning indicated that the sample mean was P37, 900 and a sample standard deviation was P5, 600. At the 0.10 level of significance, is there sufficient evidence to conclude that the cost has increased?

3. Solutions:

Step 1: state the hypothesis

Ho: There is no sufficient evidence to conclude that the cost has increased.

Ha: There is sufficient evidence to conclude that the cost has increased.

Step 2: The level of significance and critical region. A = ___ and Zcritical = ___

Step 3: Compute for the value of one sample z test. Zcomputed = _________.

Step 4: Decision rule

______________________________________________________

______________________________________________________

Step 5: Conclusion

______________________________________________________

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