Question

How many hours have you slept in the last 24 hour period? (round to the nearest .25 hours)

8

__________________

A previous survey administered to high school students showed that the amount of sleep (in hours) in a 24-hour period is normally distributed with a mean of 7 hours and a standard deviation of 1.5 hours.

What is your z-score?

What percentage of high school students from the survey slept less than you?

3. What percentage of high school students from the survey slept more than you?

Kyle says he slept 8.75 hours. What was Kyle’s z-score? What does this mean?

What percentile is Kyle in? What does this mean?

Your principal comes into the class and announces he slept 7.25 hours. What is the principal’s z-score?

What percent of high school students from the survey slept longer than the principal?

What percentage of students slept between the principal and Kyle’s sleep times?

9. What percent of data in the survey lies in the interval 5.5 to 8.5 hours?

10. What interval about the mean includes 95% of the data in the survey?

How many hours have you slept in the last 24 hour period? (round to the nearest .25 hours)

8

__________________

A previous survey administered to high school students showed that the amount of sleep (in hours) in a 24-hour period is normally distributed with a mean of 7 hours and a standard deviation of 1.5 hours.

What is your z-score?

What percentage of high school students from the survey slept less than you?

3. What percentage of high school students from the survey slept more than you?

Kyle says he slept 8.75 hours. What was Kyle’s z-score? What does this mean?

What percentile is Kyle in? What does this mean?

Your principal comes into the class and announces he slept 7.25 hours. What is the principal’s z-score?

What percent of high school students from the survey slept longer than the principal?

What percentage of students slept between the principal and Kyle’s sleep times?

9. What percent of data in the survey lies in the interval 5.5 to 8.5 hours?

10. What interval about the mean includes 95% of the data in the survey?

Answer 1

How many hours have you slept in the last 24 hour period?

8 hours

My is your z-score is,

z = 0.6667

Percentage of high school students from the survey slept less than you is,

P(x < 8) = P(z < 0.6667)

= 0.7454

= 74.54%

Percentage of high school students from the survey slept more than you

P(x > 8) = 1 - P(z > 0.6667)

= 1 - 0.7454

= 0.2546

= 25.46%

Since, Kyle says he slept 8.75 hours. Kyle’s z-score is,

z = (8.75 - 7)/1.5

= 1.1667

This mean that Kyle is 1.667 standard deviations away from mean.  

Kyle is in 87th percentile

This means that the Kyle lies in 87th percentile of the distribution.

The principal’s z-score is,

z = (7.25 - 7)/1.5

= 0.16667

Percent of high school students from the survey that slept longer than the principal is,

P(x > 7.25) = P(z > 0.1667)

= 1 - P(z > 0.1667)

= 0.4338

Percentage of students slept between the principal and Kyle’s sleep times is,

P(7.25 < x < 8.75) = P(0.1667 < z < 1.1667)

= P(z < 1.1667) - P(z < 0.4438)

= 0.3121

= 31.21%

Percent of data in the survey lies in the interval 5.5 to 8.5 hours is,

P(5.5 < x < 8.5) = P(-1 < z < 1)

= 68.27%

The interval about the mean that includes 95% of the data in the survey is,

z score at 95% is given by 1.645

1.645 = (x-7)/1.5

x = 9.4675