A class of 90 students had a mean test score of 74 with a standard deviation of 8 points.
The test will be curved so that all students whose scores are at least 1.5 standard deviations above or below the mean will receive As and Fs, respectively.
How many students will get As and how many will get Fs?
Because the class is large, it is likely the scores have a normal distribution.
If the scores are curved:
The mean of 74 will correspond to a score of 0 in the standard normal distribution.
A score that is 1.5 standard deviations above the mean will correspond to a score of +1.5 in the standard normal distribution, while a score that is 1.5 standard deviations below the mean will correspond to a score of -1.5.
Approximately 10% of the data in a standard normal distribution lies within 1/8 of a standard deviation from the mean.
Within 1/8 means between -0.125 and 0.125.
Suppose the measurements of a certain population are normally distributed with a mean of 112 and standard deviation of 24. What values correspond to the interval given above?
Designers of a new computer mouse have learned that the lengths of women’s hands are normally distributed with a mean of 17 cm and a standard deviation of 1 cm.
What percentage of women have hands in the range from 15 cm to 19 cm?
In 1996, the finishing times for the New York City Marathon were approximately normal, with a mean of 260 minutes and a standard deviation of about 50 minutes.
What percentage of the finishers that year had times between 285 minutes and 335 minutes.
But our question asked if an HDL level of 40 mg/dL or below signals an increased risk for coronary heart disease, what percentage of the women studied are at increased risk? Solution: We need the area to the left of -1.6 is 0.5 – 0.4452 = 0.0548.
In this group of women, 5.48% of them are at increased risk for coronary heart disease because of low HDL levels.
If samples of size n are taken from a population having a population proportion p , then the set of all sample proportions has a mean and standard deviation of:
Fox News asked 900 registered voters whether or not they would take a smallpox vaccine.
Suppose it is known that 60% of all Americans would take the vaccine. What is the approximate percentage of samples for which between 58% and 62% of voters in the sample would take the shot?
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