CCHS
Chapter 5 Sections 5.1 & 5.2 Practice
Name______Date______Period______
For 1 & 2, draw a normal curve and fill in the values for the mean and 1, 2, and 3 standard deviations;
1. A Dogs Life Span ¨ The life span of a dog is normally distributed with a mean of 12.5 years and a standard deviation of 2 years. Estimate the probability that a dog’s life span is between 10.5 and 14.5 years.
2. Light Bulb Life Span ¨ The life span of a certain type of light bulb is normally distributed with a mean of 5000 hours and a standard deviation of 150 hours. Estimate the probability that this type of light bulb has a life span is between 4850 and 5300 hours.
Finding Area in Exercises 3-8, find the indicated area under the standard normal curve. (Hint: Draw a picture)
3. Between z = 0 and 1.28 4. Between z = 0 and z = -2.12
5. To the right of z = 2.40 6. To the left of z = -0.46
7. Between z = 1.23 and z = 1.90 8. Between z = -1.45 and z = 1.87
Finding Probabilities In Exercises 9-14, find the probabilities for each using the standard normal distribution.
9. P (-1.25< z < 0) 12. P (z > -0.5)
10. P (z > 2.53) 13. P (-2.05 < z < 1.85)
11. P (z < -1.25) 14. P (z < -1.54 or z > 1.54)
15. What is the total area underneath the normal curve?
16. What percentage of the area falls above the mean?
True or False.
17. The area under the curve for a normal distribution is 1. T or F
18. The mean, mode and media are all equal for a normal T or F
distribution.
19. The area under the standard normal curve that lies within T or F
two standard deviations from the mean is approximately 95%.
20. A distribution is said to be positively skewed if the mean T or F
falls to the right of the mean.
Graphical Analysis In Exercises 21-26, find the probability of z occurring in the indicated region.
21. 22.
23. 24.
26. Bags of Flour ¨ The weights of bags of flour are normally distributed, with a mean of 5 pounds (80 ounces) and a standard deviation of 0.5 ounce. Determine an interval of values into which (a) about 95% of the bags of flour will fall and (b) about 68% of the bags of flour will fall.
Chapter 6 Sections 5.1 & 5.2Practice
Name______Keys______Date__December 18, 2012_ Period______
For 1 & 2, draw a normal curve and fill in the values for the mean and 1, 2, and 3 standard deviations;
1. A Dogs Life Span ¨ The life span of a dog is normally distributed with a mean of 12.5 years and a standard deviation of 2 years. Estimate the probability that a dog’s life span is between 10.5 and 14.5 years.
Within one standard deviation from the mean the probability is about 68%
2. Light Bulb Life Span ¨ The life span of a certain type of light bulb is normally distributed with a mean of 5000 hours and a standard deviation of 150 hours. Estimate the probability that this type of light bulb has a life span is between 4850 and 5300 hours.
0ne standard deviation to the left or 34% and two standard deviation to the right 47.5% the sum is 81.5 %
Finding Area in Exercises 3-8, find the indicated area under the standard normal curve. (Hint: Draw a picture)
3. Between z = 0 and 1.28 4. Between z = 0 and z = -2.12
Normalcdf (0, 1.28) Normalcdf (-2.12, 0)
0.3997 0.4830
5. To the right of z = 2.40 6. To the left of z = -0.46
Normalcdf (2.40, 10) Normalcdf (-0.46, 10)
0.0082 0.6772
7. Between z = 1.23 and z = 1.90 8. Between z = -1.45 and z = 1.87
Normalcdf (1.23, 1.90) Normalcdf (-1.47, 1.87)
0.0806 0.8985
Finding Probabilities In Exercises 9-14, find the probabilities for each using the standard normal distribution.
9. P(-1.25< z < 0) 12. P(z > -0.5)
Normalcdf(-1.25, 0) Normalcdf -0.5, 10)
0.3944 0.6915
10. P(z > 2.53) 13. P(-2.05 < z < 1.85)
Normalcdf (2.53, 10) Normalcdf (-2.05, 1.85)
0.0057 0.9477
11. P(z < -1.25) 14. P(z < -1.54 or z > 1.54)
Normalcdf (-10, -1.25) Normalcdf (-10,-1.54) + Normalcdf (1.54,10)
0.1056 0.1236
15. What is the total area underneath the normal curve? 1 or 100%
16. What percentage of the area falls above the mean? 50%
True or False.
17. The area under the curve for a normal distribution is 1. T or F
18. The mean, mode and media are all equal for a normal T or F
distribution.
19. The area under the standard normal curve that lies within T or F
two standard deviations from the mean is approximately 95%.
20. A distribution is said to be positively skewed if the mean T or F
falls to the right of the mean.
Graphical Analysis In Exercises 21-26, find the probability of z occurring in the indicated region.
21. Normalcdf (0, 2.25) 22. 2* Normalcdf (1.29, 10)
0.4878 0.0985
23. Normalcdf (-10, 1.27) 24. Normalcdf (-0.87, 10)
0.8980 0.8078
26. Bags of Flour ¨ The weights of bags of flour are normally distributed, with a mean of 5 pounds (80 ounces) and a standard deviation of 0.5 ounce. Determine an interval of values into which (a) about 95% of the bags of flour will fall and (b) about 68% of the bags of flour will fall.
a/ 95% 80 – 2*0.5 = 79 ounces 80+2*0.5 = 81 ounces within 79 and 81 ounces
b/79.5 and 80.5 ounces for 68%
Mambou 9:43:46 AM 12/18/2012