Math 116
Math 116 - Chapter 6 review Name___________________________________
Provide an appropriate response. 1)
Two random variables are normally distributed with the same mean. One has a standard deviation of 10 while the other has a standard deviation of 15. How will the graphs of the two variables differ and how will they be alike? 2)
Which is larger, the area under the standard normal curve between -1 and 1, or the area under the standard normal curve between 0 and 2? Explain your reasoning. 3)
Which of the variables below do you think will be roughly normally distributed?
a. Weights of 10 year old boys
b. Incomes of 40 year old adults
c. The numbers that show up when you roll a balanced die
d. The amount of coffee which a filling machine puts into "4 ounce jars"
Fill in the blanks by standardizing the normally distributed variable. 4)
Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 42 minutes and a standard deviation of 4 minutes. The percentage of time that his commute time lies between 50 and 54 minutes is equal to the area under the standard normal curve between ___ and ___.
Use a table of areas to find the specified area under the standard normal curve. 5)
The area that lies between 0 and 3.01 6)
The area that lies between -1.10 and -0.36
Use a table of areas for the standard normal curve to find the required z-score. 7)
Find the z-score for having area 0.07 to its right under the standard normal curve, that is, find [pic]. 8)
Find the z-score for which the area under the standard normal curve to its left is 0.04 9)
Determine the two z-scores that divide the area under the standard normal curve into a middle 0.874 area and two outside 0.063 areas.
Find the indicated probability or percentage for the normally distributed variable. 10)
The variable X is normally distributed. The mean is μ = 15.2 and the standard deviation is σ = 0.9.
Provide an appropriate response. 1)
Two random variables are normally distributed with the same mean. One has a standard deviation of 10 while the other has a standard deviation of 15. How will the graphs of the two variables differ and how will they be alike? 2)
Which is larger, the area under the standard normal curve between -1 and 1, or the area under the standard normal curve between 0 and 2? Explain your reasoning. 3)
Which of the variables below do you think will be roughly normally distributed?
a. Weights of 10 year old boys
b. Incomes of 40 year old adults
c. The numbers that show up when you roll a balanced die
d. The amount of coffee which a filling machine puts into "4 ounce jars"
Fill in the blanks by standardizing the normally distributed variable. 4)
Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 42 minutes and a standard deviation of 4 minutes. The percentage of time that his commute time lies between 50 and 54 minutes is equal to the area under the standard normal curve between ___ and ___.
Use a table of areas to find the specified area under the standard normal curve. 5)
The area that lies between 0 and 3.01 6)
The area that lies between -1.10 and -0.36
Use a table of areas for the standard normal curve to find the required z-score. 7)
Find the z-score for having area 0.07 to its right under the standard normal curve, that is, find [pic]. 8)
Find the z-score for which the area under the standard normal curve to its left is 0.04 9)
Determine the two z-scores that divide the area under the standard normal curve into a middle 0.874 area and two outside 0.063 areas.
Find the indicated probability or percentage for the normally distributed variable. 10)
The variable X is normally distributed. The mean is μ = 15.2 and the standard deviation is σ = 0.9.