The answer is B because the quantity tends to stay the same as the sample goes up
Substitute
, so that
. The integral is then equivalent to
Then transforming back to
gives
The percentage of young adults send between 128 and 158 text messages per day is; 34%
<h3>How to find the percentage from z-score?</h3>
The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.
We are given;
Sample mean; x' = 158
Population mean; μ = 128
standard deviation; σ = 30
We want to find the area under the curve from x = 248 to x = 158.
where x is the number of text messages sent per day.
To find P(158 < x < 248), we will convert the score x = 158 to its corresponding z score as;
z = (x - μ)/σ
z = (158 - 128)/30
z = 30/30
z = 1
This tells us that the score x = 158 is exactly one standard deviation above the mean μ = 128.
From online p-value from z-score calculator, we have;
P-value = 0.34134 = 34%
Approximately 34% of the the population sends between 128 and 158 text messages per day.
Read more about p-value from z-score at; brainly.com/question/25638875
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