(1) Evaluate the following probabilities based on the standard normal distribution: Round all answers to 4 decimal places.

a. P(z<1.5)=P(z<1.5)= b. P(z>1.8)=P(z>-1.8)= c. P(1.40.6)=P(z>0.6)=

(2) For a 4-period class, students should spend an 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. 68% of the students have study hours that are between and

(3) Given a set of data that is bell-shaped, there is approximately _____ % of the data within 3 standard deviations. Fill in the blank with the best answer:

• 0
• 68
• 75
• 89
• 95
• 99.7

(4) Time spent on a math assignment appears fairly bell shaped with a mean of 94 minutes and standard deviation of 16 minutes. Use the empirical rule to answer the following questions: a) Approximately 68% of the students spent between and minutes on the assignment. b) Approximately 99.7% of the students spent between and minutes on the assignment.

(5) 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 ?

(6) Use the Empirical Rule.

Draw a sketch of the normal distribution and label the mean and 1, 2, and 3 standard deviations 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? ?

(7) Find the following Z scores, reporting to 1 decimal place.

A. The area between a negative z and 0 is 0.4554

B. The area between a positive z and 0 is 0.1179