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The distribution of the amount of money spent on book purchases for a semester by college students has a mean of $280 and a standard deviation of $40. If the distribution is bell-shaped and symmetric, what proportion of students will spend between $200 and $280 this semester? Round your answer to four decimal places.

Respuesta :

JeanaShupp

Answer: 0.4772

Step-by-step explanation:

Given : The distribution is bell shaped , then the distribution must be normal distribution.

Mean : [tex]\mu=\$280[/tex]

Standard deviation :[tex]\sigma= \$40[/tex]

The formula to calculate the z-score :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x = $200

[tex]z=\dfrac{200-280}{40}=-2[/tex]

For x = $280

[tex]z=\dfrac{280-280}{40}=0[/tex]

The p-value = [tex]P(-2<z<0)=P(z<0)-P(z<-2)[/tex]

[tex]0.5-0.0227501=0.4772499\approx0.4772[/tex]

Hence, the proportion of students will spend between $200 and $280 this semester = 0.4772