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The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester?

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Answer:

Almost 2.5% of the students spent more than $275 in a semester.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 235

Standard deviation = 20

According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester?

95% of the measures are within 2 standard deviation of the mean. The other 5% are more than 2 standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of those are below two standard deviations of the mean and 2.5% are more than two standard deviations above the mean.

235 + 2*20 = $275

Almost 2.5% of the students spent more than $275 in a semester.

2.5% of students spent more than 274.2 on textbooks.

Given that

The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20.

We have to determine

According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester?

According to the question

A mean of $235 and a standard deviation of $20.

The distribution of the amount of money spent by students on textbooks in a semester are approximately normal in shape with a mean of μ = 382 and a standard deviation of σ = 21

We need to find according to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester.

[tex]\rm P(x) =\dfrac{ 2.5}{100} = 0.025\\\\ P(x > ?) = 1 - P(z > ?)\\\\0.025 = 1 - P(z > ?) \\\\P(z > ?) = 1 - 0.025 = 0.975[/tex]

The corresponding value for the area of 0.975 from the normal distribution table.

The value of z corresponding to 0.975 = 1.96

x = μ + zσ

μ = 235 and σ= 20

x = 235 + 1.96 × 20 = 235 + 39.2 = 274.2

The amount of money is 274.2.

Hence, 2.5% of students spent more than 274.2 on textbooks.

To know more about Confidence intervals click the link given below.

https://brainly.com/question/3041663