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?

2.5% of students spent more than 274.2 on textbooks.

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?

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.

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.

link

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.

215.92 dollars is the answer

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!