Concept explainers
Find the standard normal area for each of the following, showing your reasoning clearly and indicating which table you used.
- a. P(−1.22 < Z < 2.15)
- b. P(−3.00 < Z < 2.00)
- c. P(Z < 2.00)
- d. P(Z = 0)
a.
Find the standard normal area for
Answer to Problem 17SE
The standard normal area for
Explanation of Solution
Calculation:
Normal distribution:
A continuous random variable X is said to follow normal distribution if the probability density function of X is,
Standard normal distribution:
A continuous random variable Z is said to follow standard normal distribution if the probability density function of Z is,
For a standard normal variable it is known that,
The probability
Calculate the value of
From Appendix C-1: Table “STANDARD NORMAL AREAS”,
- Locate the z value 2.1 in column of z.
- Locate the probability value corresponding to z-value 2.1 in the column 0.05.
Thus,
Calculate the value of
From Appendix C-2: Table “CUMULATIVE STANDARD NORMAL DISTRIBTION”,
- Locate the z value –1.2 in column of z.
- Locate the probability value corresponding to z-value –1.2 in the column 0.02.
Thus,
Hence,
Hence, the standard normal area for
b.
Find the standard normal area for
Answer to Problem 17SE
The standard normal area for
Explanation of Solution
Calculation:
For a standard normal variable it is known that,
The probability
Calculate the value of
From Appendix C-1: Table “STANDARD NORMAL AREAS”,
- Locate the z value 2.0 in column of z.
- Locate the probability value corresponding to z-value 2.0 in the column 0.00.
Thus,
Calculate the value of
From Appendix C-2: Table “CUMULATIVE STANDARD NORMAL DISTRIBTION”,
- Locate the z value –3.0 in column of z.
- Locate the probability value corresponding to z-value –3.0 in the column 0.00.
Thus,
Hence,
Hence, the standard normal area for
c.
Find the standard normal area for
Answer to Problem 17SE
The standard normal area for
Explanation of Solution
Calculation:
For a standard normal variable it is known that,
The probability
From part (b), it is found that
Hence,
Hence, the standard normal area for
d.
Find the standard normal area for
Answer to Problem 17SE
The standard normal area for
Explanation of Solution
Calculation:
Calculate the value of
From Appendix C-1: Table “STANDARD NORMAL AREAS”,
- Locate the z value 0.00 in column of z.
- Locate the probability value corresponding to z-value 0.00 in the column 0.00.
Thus,
Moreover, it can be said that in case of continuous distribution the probability value for a particular point is 0.
Therefore, the standard normal area for
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Chapter 7 Solutions
APPLIED STAT.IN BUS.+ECONOMICS
- Dr. Seboo has collected the total cholesterol levels of all his patients. He is trying to figure what the typical cholesterol level falls. Use the following output to answer the questions. a. What variable was recorded in the data collected? Classify the variable as categorical or quantitative.Variable: ______________________ Circle one: Categorical or Quantitativeb. Describe the shape of the above distribution:c. The average cholesterol level was _______________, and 50% of this sample cholesterol levels was ________________ or more. The minimum cholesterol level was _______________, while the maximum number cholesterol level was _________________. The middle 50% of cholesterol levels in this sample were between ______________ and ______________. According to _____________________________ Rule, we expect ________% of the cholesterol levels to be between ________________ and _______________ (two standard deviations from the mean).d. Construct a 95% confidence interval for the mean…arrow_forwardWhat is the p value and z value?arrow_forward
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