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Alchen [17]
3 years ago
10

The cell phone bill recorded that Jeremiah sent 532 text messages last week. On average

Mathematics
2 answers:
nadezda [96]3 years ago
8 0

Answer:

76 sent text messages per day.

Step-by-step explanation:

The question above is answered below.

Average of a dataset is obtained by the ratio of total sum of dataset and number of observations.

In this case, average text messages sent equals total sent text messages divide by number of days in a week. Thus:

average =  \frac{532}{7}

average = 76 \: text \: messages

Having recorded 532 sent text messages last week; on average, Jeremiah sent 76 text messages each day.

Kipish [7]3 years ago
7 0

Answer: 76

Step-by-step explanation:

create an equation

the average each day is how many messages there are each day, so you would divide the total messages evenly to get the messages per day

average = total message / num days

finding values to use in formula

the total messages is given = 532

num days = 7 because there are 7 days in a week

plug in to solve

solving the formula

average = total messages/num day

average = 532/7 = 76

final answer

76 text messages each day

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Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

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Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find the margin of error M as such

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In which \sigma is the standard deviation of the population and n is the size of the sample. In this problem, \sigma = 0.25

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M = z*\frac{\sigma}{\sqrt{n}}

0.1 = 1.96*\frac{0.25}{\sqrt{n}}

0.1\sqrt{n} = 1.96*0.25

\sqrt{n} = \frac{19.6*0.25}{0.1}

(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.1})^{2}

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Rounding up to the nearest whole number, 25.

(b) The desired margin of error is $0.06.

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0.06 = 1.96*\frac{0.25}{\sqrt{n}}

0.06\sqrt{n} = 1.96*0.25

\sqrt{n} = \frac{19.6*0.25}{0.06}

(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.06})^{2}

n = 66.7

Rounding up, 67

(c) The desired margin of error is $0.05.

This is n when M = 0.05. So

M = z*\frac{\sigma}{\sqrt{n}}

0.05 = 1.96*\frac{0.25}{\sqrt{n}}

0.05\sqrt{n} = 1.96*0.25

\sqrt{n} = \frac{19.6*0.25}{0.05}

(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.05})^{2}

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Rounding up, 97

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Step-by-step explanation:

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