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3 years ago

A text message plan coasts $7 per month pluse $0.46 per text. Find the monthly cost for x text messages.

Mathematics

1 answer:

Nadya [2.5K]3 years ago

3 0

p = 7 + 0.46x is the monthly cost for x text messages

<u>Solution:</u>

Given that, A text message plan costs $7 per month plus $0.46 per text

To find: Monthly cost for "x" text messages'

Let "x" be the number of text messages in a month

From given information,

text message plan cost per month = $ 7

Cost for 1 text = $ 0.46

Let "p" be the Monthly cost for "x" text messages

Then, we get,

p = text message plan cost per month + (Cost for 1 text)(number of text messages in a month)

$p = 7 + 0.46x$

Thus the monthly cost for x text messages is found

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The time needed to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes

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Answer:

a. The probability of completing the exam in one hour or less is 0.0783

b. The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

c. The number of students will be unable to complete the exam in the allotted time is 8

Step-by-step explanation:

a. According to the given we have the following:

The time for completing the final exam in a particular college is distributed normally with mean (μ) is 77 minutes and standard deviation (σ) is 12 minutes

Hence, For X = 60, the Z- scores is obtained as follows:

Z= X−μ /σ

Z=60−77 /12

Z=−1.4167

Using the standard normal table, the probability P(Z≤−1.4167) is approximately 0.0783.

P(Z≤−1.4167)=0.0783

Therefore, The probability of completing the exam in one hour or less is 0.0783.

b. In this case For X = 75, the Z- scores is obtained as follows:

Z= X−μ /σ

Z=75−77 /12

Z=−0.1667

Using the standard normal table, the probability P(Z≤−0.1667) is approximately 0.4338.

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is obtained as follows:

P(60<X<75)=P(Z≤−0.1667)−P(Z≤−1.4167)

=0.4338−0.0783

=0.3555

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

c. In order to compute how many students you expect will be unable to complete the exam in the allotted time we have to first compute the Z−score of the critical value (X=90) as follows:

Z= X−μ /σ

Z=90−77 /12

Z=1.0833

UsING the standard normal table, the probability P(Z≤1.0833) is approximately 0.8599.

Therefore P(Z>1.0833)=1−P(Z≤1.0833)

=1−0.8599

=0.1401

Therefore, The number of students will be unable to complete the exam in the allotted time is= 60×0.1401=8.406

The number of students will be unable to complete the exam in the allotted time is 8

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3 years ago

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