Download Math Tech IV Chapter 5 Sections 5

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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)
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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
distribution.
T
or
F
19. The area under the standard normal curve that lies within
two standard deviations from the mean is approximately 95%.
T
or
F
20. A distribution is said to be positively skewed if the mean
falls to the right of the mean.
T
or
F
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.
Mambou
1:42:42 PM
6/24/2017
CCHS
Chapter 6 Sections 5.1 & 5.2Practice
Name___________________Keys_____________________ Date__June 24, 2017_ 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
Normalcdf (0, 1.28)
0.3997
4. Between z = 0 and z = -2.12
Normalcdf (-2.12, 0)
0.4830
5. To the right of z = 2.40
Normalcdf (2.40, 10)
0.0082
6. To the left of z = -0.46
Normalcdf (-0.46, 10)
0.6772
7. Between z = 1.23 and z = 1.90
Normalcdf (1.23, 1.90)
0.0806
8. Between z = -1.45 and z = 1.87
Normalcdf (-1.47, 1.87)
0.8985
Finding Probabilities In Exercises 9-14, find the probabilities for each using the standard normal
distribution.
9. P(-1.25< z < 0)
Normalcdf(-1.25, 0)
0.3944
12. P(z > -0.5)
Normalcdf -0.5, 10)
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.
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CCHS
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
distribution.
T or F
19. The area under the standard normal curve that lies within
two standard deviations from the mean is approximately 95%.
T or F
20. A distribution is said to be positively skewed if the mean
falls to the right of the mean.
T or F
Graphical Analysis In Exercises 21-26, find the probability of z occurring in the indicated region.
21.
Normalcdf (0, 2.25)
0.4878
23.
Normalcdf (-10, 1.27)
0.8980
22.
2* Normalcdf (1.29, 10)
0.0985
24.
Normalcdf (-0.87, 10)
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%
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1:42:42 PM
6/24/2017