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The ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years. Approximately what percent of the students are between 14 and 18 years old?

a. 24.17%

b. 62.47%

c. 30.85%

d. 93.32%

I've tried solving this, and I ended up with z-scores -0.5 for 14-year-olds and 1.5 for 18-year-olds. And I also matched them using a chart and got "0.3085" and "0.9332", but I don't know if I should add or subtract because, in a similar problem I had to add but if I add the percentages, it exceed 100%. I am confused; please help!!

Respuesta :

isyllus

Answer:

B) 62.47% of the students are between 14 and 18 years old.

Step-by-step explanation:

Mean = 15 and Standard deviation = 2

Student between 14 to 18

Formula used z-score

[tex]z=\frac{X-\bar{x}}{\sigma}[/tex]

For age 14 , z score

[tex]X=14,\bar{x}=15,\sigma=2[/tex]

[tex]z=\frac{14-15}{2}\Rightarrow -0.5[/tex]

Using z-table , P(z>-0.5)=0.3085

For age 18 , z score

[tex]X=18,\bar{x}=15,\sigma=2[/tex]

[tex]z=\frac{18-15}{2}\Rightarrow 1.5[/tex]

Using z-table , P(z<1.5)=0.9332

P(-0.5<z<1.5)=0.9332-0.3085 = 0.6247

Thus, 62.47% of the students are between 14 and 18 years old.

Answer:

62.7 are 14 and 18 years old

Swtep-by-step explanation:

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