Math 136 Ch 6 Lab Normal Distribution 1. State the Empirical Rule for Normal Distributions. Fill in the blanks. a. Approximately ____% of the data lie with ____ standard deviation of the mean. b. Approximately ____% of the data lie with ____ standard deviations of the mean. c. Approximately ____% of the data lie with ____ standard deviations of the mean. 2. Class test scores are normally distributed with mean 64 and standard deviation of 10. Find the percent of scores using the Empirical Rule. Make a sketch for each problem shading the desired area. a. $X > 74$ b. $44 < X < 74$ c. $X < 44$ 3. Class test scores are normally distributed with mean 64 and standard deviation of 10. Find the probability of scores using GeoGebra. Round to four decimal places. Make a sketch for each problem shading the desired area. a. $P(X > 90)$ b. $P(50 < X < 90)$ c. $P(X < 50)$
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Approximately 68% of the data lie within one standard deviation of the mean. b. Approximately 95% of the data lie within two standard deviations of the mean. c. Approximately 99.7% of the data lie within three standard deviations of the mean. Show more…
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1. For a normal curve whose mean is 5 with a standard deviation of 1.1, find the x-value with 73% of the data to the left of it. a) 5.67 b) 0.61 c) 0.73 d) answer not here 2. The marks on a statistics test are normally distributed with a mean of 62 and a standard deviation of 15. If the instructor wishes to assign B's or higher to the top 30% of the students in the class, what mark is required to get a B or higher? You must get a 69.8 to get a B or higher. True False 3. Find the area under the normal distribution curve to the right of z = -0.65. a) 74% b) 24% c) 26% d) -24% 4. Given the normal distribution curve shown in the figure below, find the area under the curve between z = 0 and z = 2.16. a) 48.21% b) 48.46% c) 47.88% d) 49.55% 5. Find the probability P(z < 0.17) using the standard normal distribution. (Remember probability is the same thing as the area for the normal curve.) a) 0.5675 b) 0.0675 c) 0.4325 d) 0.8300 6. Find the area under the normal distribution curve between z = -0.85 and z = 1.95. a) 30% b) 47% c) 17% d) 78% 7. Find the probability P(-0.62 < z < -0.01) using the standard normal distribution. a) 0.7716 b) 0.3584 c) 0.2284 d) 0.1900 8. For a normal curve whose mean is 2.1 with a standard deviation of 0.5, find the area underneath the curve with x less than 2.2. a) 58% b) 42% c) 2.2% d) answer not here 9. For a normal curve whose mean is 5 with a standard deviation of 1.1, find the x-value with 73% of the data to the left of it. a) 5.67 b) 0.61 c) 0.73 d) answer not here
Adi S.
A normal distribution has which of the following properties? a. It is symmetric. b. All three measures of central tendency are equal in this distribution. c. It has more than one mode. d. A and B only. e. All of the above. The variance of the standard normal curve is equal to ______. a. 0 b. The standard deviation of the standard normal curve. c. The mean of the standard normal curve. d. There is not enough information given to answer. Birth weights at a local hospital are normally distributed with a mean of 110 oz. and a standard deviation of 15 oz. The proportion of infants with birth weights above 125 oz. is: a. 0.1379 b. 0.8413 c. 0.4602 d. None of these choices are correct. Using the standard normal distribution tables, the area under the standard normal curve corresponding to -0.50 < Z < 1.20 is: a. 0.3085 b. 0.8849 c. 0.5764 d. 0.2815 Using the standard normal distribution tables, find the value of Z so that the percentage of observations that are less than Z in a standard normal distribution is 30.5%. a. Z = -1.81 b. Z = 2.70 c. Z = 0.6915 d. Z = -0.51 In recent years, scores on the verbal section of the SAT have followed a normal distribution with a mean of 515 and a standard deviation of 109. How high must a student score in order to achieve the 95th percentile for this section of the SAT? Please show work whenever possible.
Kari H.
5- In its standardized form, the normal distribution a- has an area less than 1. b- has a mean of 0 and a standard deviation of 1. c- has a mean of 0 and a variance of 1. d- has an area equal to 0.5. 6- Which of the following about the normal distribution is not true? a- Theoretically, the mean, median, and mode are the same. b- About 2/3 of the observations fall within ±1 standard deviation from the mean. c- Its parameters are the mean, μ and standard deviation, σ. d- It has an area more than 1. 7- The value of the cumulative standardized normal distribution at Z is 0.8770. What is the value of Z ? (Hint: Use the Z table or NORM.S.INV function in excel) a- 0.18. b- 1.47. c- 0.81. d- 1.16. 8- Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 46 and 54. (Hint: NORM.S.DIST(-1,TRUE)=0.1587, NORM.S.DIST(1,TRUE)=0.8413, NORM.S.DIST(-2,TRUE)=0.02275 and NORM.S.DIST(2,TRUE)=0.97725) a- 0.97725 b- 0.8413 c- 0.6826 d- 0.9545 9- The standard error of the mean a- is never larger than the standard deviation of the population. b- measures the variability of the mean from sample to sample. c- decreases as the sample size increases. d- All of the above. 10- Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect? a- The standard deviation of the sampling distribution is equal to 3 years. b- The mean of the sampling distribution is equal to 23 years. c- The standard error of the sampling distribution is equal to 0.3 years. d- The shape of the sampling distribution is approximately normal. 11- Which of the following statistics is not a measure of central tendency? a- mode b- Q3 c- median d- arithmetic mean. 12- In a perfectly symmetrical distribution, a- the median equals the arithmetic mean. b- the variance equals the standard deviation. c- the interquartile range equals the arithmetic mean. d- the range equals the interquartile range.
Chai S.
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