The figure below will help you to visualize the 68-95-99.7 Rule (or the Empirical Rule) for a Normal Distribution.[br]The histogram displays 100 data values from a population N(0,1).[br]The histogram is centered on the mean of the data.[br]The width of each bin is the standard deviation of the data. Therefore, the bin boundaries are z-scores.[br]The numbers on each bin is the number of data values in the bin. Since there are 100 data values, these numbers[br]are percents.
1. For the distribution N(155, 9), use the empirical rule (68-95-99.7 rule) to determine the percent of data values between 138 and 155.
2. What is the percentage of a normal distribution that is less than the mean?
3. For a normal model with mean 9.7 and a standard deviation of 1.2, what proportion of data values are greater than 10?
4. The age of student in a community college is normally distributed with a mean of 30 years and standard deviation σ = 4 years. Let X represent the age of a randomly selected student. Find[br]a) P(x < 40) [br]b) P(x > 21) [br]c) P(30 < x < 35)
a) 0.9938, [br]b) 0.9878[br]c) 0.3944
5. Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admitted to this university?
a) Yes, because he scored better than 80.23% of the students who took the test.