Question

problem solving the numbers of text messages sent and received in one day by a random sample of 30 teen cell phone users are shown in the table.
number of text messages
35 65 64 88 46
42 71 68 65 97
58 47 52 37 84
58 85 46 56 90
78 76 74 36 74
62 65 75 96 72
a. estimate the population proportion of teen cell phone users who send and receive more than 70 text messages each day.
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b. estimate the population proportion of teen cell phone users who send and receive fewer than 50 text messages each day.
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Explanation:

Step1: Count numbers >70 (for part a)

List of numbers >70: 88, 71, 97, 84, 85, 90, 78, 76, 74, 74, 65 (wait, 65<70, no), 75, 96, 72. Wait, let's list all 30 numbers:

Row 1: 35, 65, 64, 88, 46 (1 number >70: 88)
Row 2: 42, 71, 68, 65, 97 (2 numbers: 71, 97)
Row 3: 58, 47, 52, 37, 84 (1 number: 84)
Row 4: 58, 85, 46, 56, 90 (2 numbers: 85, 90)
Row 5: 78, 76, 74, 36, 74 (4 numbers: 78, 76, 74, 74)
Row 6: 62, 65, 75, 96, 72 (3 numbers: 75, 96, 72)

Total for part a: 1+2+1+2+4+3 = 13? Wait, let's count again carefully:

All numbers:
35, 65, 64, 88, 46,
42, 71, 68, 65, 97,
58, 47, 52, 37, 84,
58, 85, 46, 56, 90,
78, 76, 74, 36, 74,
62, 65, 75, 96, 72.

Now check each for >70:

88: yes (1)
71: yes (2)
97: yes (3)
84: yes (4)
85: yes (5)
90: yes (6)
78: yes (7)
76: yes (8)
74: yes (9)
74: yes (10)
75: yes (11)
96: yes (12)
72: yes (13)
Wait, 71,97,88,84,85,90,78,76,74,74,75,96,72. Wait, that's 13? Wait row 2: 71,97 (2), row1:88 (1), row3:84 (1), row4:85,90 (2), row5:78,76,74,74 (4), row6:75,96,72 (3). 1+2+1+2+4+3=13. Total sample size n=30. So proportion for a: 13/30 ≈0.433 (or 43.3%).

Step2: Count numbers <50 (for part b)

Numbers <50: 35, 46, 42, 47, 37, 46, 36.

Row1: 35, 46 (2)
Row2: 42 (1)
Row3: 47, 37 (2)
Row4: 46 (1)
Row5: 36 (1)
Row6: none.

Total: 2+1+2+1+1 = 7. So proportion: 7/30 ≈0.233 (or 23.3%).

Answer:

(part a and b):
a. About $\frac{13}{30} \approx 0.43$ (or 43%)
b. About $\frac{7}{30} \approx 0.23$ (or 23%)

(Note: If counting was wrong, recheck. Let's recount part a:

Numbers >70: 88,71,97,84,85,90,78,76,74,74,75,96,72. Wait, 88,71,97,84,85,90,78,76,74,74,75,96,72. That's 13 numbers. 13/30 ≈0.433.

Part b: numbers <50: 35,46,42,47,37,46,36. That's 7 numbers. 7/30≈0.233.)