![]() ![]() According to the 68-95-99.7 rule, what percentage of adults are considered retarded by this criterion? People with WAIS scores below 70 are considered mentally retarded. The scale is approximately normal with mean 100 and standard deviation 15. The Wechsler Adult Intelligence scale (WAIS) is a commonly used IQ test. Which one is more likely? exceeds 70 or exceeds 70.Which one is more likely? exceeds 90 or exceeds 90.Which one is more likely? exceeds 80 or exceeds 80.Use the 68-95-99.7 rule to determine the following. Suppose that is a normal random variable with mean 80 and standard deviation 10. Suppose that is a normal random variable with mean 80 and standard deviation 5. If the proportion of female adults who are shorter than 67 inches is 0.84, determine. Heights of female adults in the United States are normally distributed with mean inches and standard deviation 2.5 inches. The proportion of male adults whose height is between 69.1 inches and 77.2 inches.The proportion of male adults whose height is between 61.0 inches and 71.8 inches.The proportion of male adults whose height is between 66.4 inches and 74.5 inches.Use the 98-95-99.7 rule to estimate the following: Heights of male adults in the United States are normally distributed with mean 69.1 inches and standard deviation 2.7 inches. ![]() How long must the length of a pregnancy is for it to fall in the longest 2.5% of all human pregnancies?.How short must the length of a pregnancy is for it to fall in the shortest 2.5% of all human pregnancies?.The middle 95% of the lengths of all pregnancies fall between which two values?.The proportion of the lengths of pregnancies that fall between 250 days and 282 days.Use the 68-95-99.7 rule to estimate the following: ![]() The length of human pregnancies from conception to birth is normally distributed with mean 266 days and standard deviation 16 days. The following is a set of 10 practice problems to reinforce the 68-95-99.7 rule. The 68-95-99.7 rule suggests that converting to z-scores is a great way to evaluate the likelihood of data points if the underlying distribution is a normal distribution. A z-score of an observation is called the standardized value. In the exam scores example discussed in the preceding paragraph, the exam score of 80 has a z-score of 2 and the exam score of 60 has a z-score of -2. In fact, the number of standard deviations away from the mean for an observation is called the z-score of that observation. So in this particular statistics course, a score of 80 or higher is significant achievement.Īs the 68-95-99.7 rule shows, all normal distributions are the same if the observations are measured in units of the standard deviation from the mean. Since the normal bell curve is symmetric, approximately 2.5% of the scores are greater than 80. On the other hand, there is only a 5% chance that a score is higher than 80 or lower than 60. Thus all the exam takers score between 55 and 85, except for 0.3% of the exam takers (3 in 1000). Around 99.7% of the scores are between 55 and 85. Around 95% of the scores are between 60 and 80. Then around 68% of the scores are between 65 and 75. Ī quick example, suppose the exam scores in a statistics course follow a normal distribution with mean 70 and standard deviation 5.
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