Question

4. To be considered as a menu item for Gloria's new restaurant an item must have scored in the top 15% by the food critics in the area. The average item's score is 7 with a standard deviation of 2. Assuming that the variable is normally distributed, find the lowest score possible for a menu item to still be considered.

5. The average number of absences for a high school senior is 5 days per school year with a standard deviation of 3. Any student whose absences who fall in the upper 10% may be at risk for failure. How many absences must a senior have to be at the risk of failure due to absences? Assume that the distribution is normal and round your answer to the nearest day.

6. The faculty at a particular school have attended up to an average 4 years of college with a standard deviation of 2 years. Faculty members who are in the lower 10% of the distribution will be offered the opportunity to obtain additional training. A faculty member must have attended less than ________ years of school to qualify for the training. Round your answer to the nearest year.

7. For a medical study, a researcher will select participants from the middle 30% of the distribution based on hours of sleep per night. If the average number of hours of sleep per night is 6 and the standard deviation is .5 hours, then between which two amounts of hours of sleep will a participant have to get to participate in the study?

Answer 1

Answer:

4. To be considered as a menu item for Gloria's new restaurant an item must have scored in the top 15% by the food critics in the area. The average item's score is 7 with a standard deviation of 2. Assuming that the variable is normally distributed, find the lowest score possible for a menu item to still be considered.

Z value for top 15% is 1.036

X= mean+z*sd = 7+ 1.036*2

=9.072

5. The average number of absences for a high school senior is 5 days per school year with a standard deviation of 3. Any student whose absences who fall in the upper 10% may be at risk for failure. How many absences must a senior have to be at the risk of failure due to absences? Assume that the distribution is normal and round your answer to the nearest day.

Z value for top 10% is 1.282

X= mean+z*sd = 5+1.282*3 =8.846

=9 ( rounded)

6. The faculty at a particular school have attended up to an average 4 years of college with a standard deviation of 2 years. Faculty members who are in the lower 10% of the distribution will be offered the opportunity to obtain additional training. A faculty member must have attended less than ________ years of school to qualify for the training. Round your answer to the nearest year.

Z value for bottom 10% is -1.282

X= mean+z*sd = 4-1.282*2 =1.436

=1 year ( rounded)

7. For a medical study, a researcher will select participants from the middle 30% of the distribution based on hours of sleep per night. If the average number of hours of sleep per night is 6 and the standard deviation is .5 hours, then between which two amounts of hours of sleep will a participant have to get to participate in the study?

Z values for middle 30% is (-0.385, 0.385)

Lower limit X= mean+z*sd = 6-0.385*0.5 = 5.8075

= 5.81( two decimals)

Upper limit X= mean+z*sd = 6+0.385*0.5 = 6.1925

= 6.19( two decimals).