6.2 HW Normal Probability Distribution, Empirical rule 8 questions

The time to complete an exam is approximately Normal with a mean of 38 minutes and a standard deviation of 8 minutes.

The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the indicated boxes.

μ=38

σ=8

Question 2

Watch this Khan Academy Empirical Rule video:

https://www.youtube.com/watch?v=OhRr26AfFBU

Use the Empirical Rule. (Do not use technology. Technology will give a slightly different answer.)

Draw a sketch of the normal distribution and label the mean and 1, 2, and 3 standard devitons above and below the mean with computed values.

Assume that the weight of 1-year-old girls in the USA is normally distributed with Mean = 9.5 kg, Standard Deviation = 1.1 kg.

(a) 68% of the data is between which 2 values? kg -- kg

(b) 95% of the data is between which 2 values? kg -- kg

(c) What percentage of the data is less than 8.4 kg? %

(d) What percentage of the data is between 7.3 kg and 11.7 kg? ?

(w) What percentage of the data is more than 12.8 kg? ?

Question 4

For a 4-units class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on students, and the distribution of total study hours per week is bell-shaped with a mean of 13 hours and a standard deviation of 3 hours.

Use the Empirical Rule to answer the following questions.

a) 95% of the students have study hours that are between and

c) What percentage of the students have study hours that are below 16? %

The heights of American adult males are normally distributed with a mean of 177 cm and a standard deviation of 7.4 cm. Use the Empirical Rule to find the range of heights that contain approximately

(a) 68% of the data

cm -- cm

(b) 95% of the data

cm -- cm

(c) 99.7% of the data

cm -- cm

A researcher studying frogs is investigating the distance that a certain species of frog can jump. The jump lengths appear to be approximately normally distributed with a mean of 95 inches and a standard deviation of 8 inches.

Directions: Make a sketch of the "empirical rule" for this setting.

a) What proportion of frog jumps are less than 87 inches?

(Enter a proportion as a decimal, not a %)

b) What jump lengths represent the middle 95% of frog jumps?

Between and

c) What is the probability of observing a random frog jump that is longer than 111 inches?

(Enter a proportion as a decimal, not a %)

8. The average resting heart rate of a population is 86 beats per minute, with a standard deviation of 11 bpm. Find the z-scores that correspond to each of the following heart rates. Round your answers to the nearest hundredth, if necessary.

(a) 104 bpm

z =

(b) 67 bpm

z =

Question 9

Quinn and Salvador began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Quinn took a test in Social Studies and earned a 81.5, and Salvador took a test in Science and earned a 69.8. Use the fact that all the students' test grades in the Social Studies class had a mean of 76.5 and a standard deviation of 9.5, and all the students' test grades in Science had a mean of 62.4 and a standard deviation of 8.8 to answer the following questions.

a) Calculate the z-score for Quinn's test grade.

z

=

z=

b) Calculate the z-score for Salvador's test grade.

z

=

z=

c) Which person did relatively better?

· Quinn

· Salvador

· They did equally well.

Question 10

Tevin and Josh began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Tevin took a test in Social Studies and earned a 78.6, and Josh took a test in Science and earned a 61. Use the fact that all the students' test grades in the Social Studies class had a mean of 76.9 and a standard deviation of 10.4, and all the students' test grades in Science had a mean of 61.5 and a standard deviation of 10.6 to answer the following questions.

a) Calculate the z-score for Tevin's test grade.

z

=

z=

[Round your answer to two decimal places.]

b) Calculate the z-score for Josh's test grade.

z

=

z=

[Round your answer to two decimal places.]

c) Which person did relatively better?

· Tevin

· Josh

· They did equally well.