# The Standard Normal Distribution - Page 4

Questions

- The annual snowfall in a town has a mean of 38 inches and a standard deviation of 10 inches. Last year there were 63 inches of snow. How many standard deviations from the mean is that?
- Which is better: a score of 82 on a test with a mean of 70 and a standard deviation of 8, or a score of 82 on a test with a mean of 75 and a standard deviation of 4?
- How can I tell if my data is normally distributed? Do the mean, median and mode have to be identical for it to be a normal distribution?
- Let #X# be #N(mu, sigma^2)# so that #P(X<89) = 0.90# and #P(X<94) = 0.95#. How do you find #mu# and #sigma^2#?
- Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(z>c)=.0559#, what is #c#?
- Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(z<b)=.9817#, what is #b#?
- The mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points. What is the probability that a student will score more than 1700 points?
- What is #P(z > 1.37) #?
- A set of test scores is normally distributed with a mean of 78 and a standard deviation of 4.5. Dwayne scored 87 on the test. What is his percentile score?
- A set of data has a normal distribution with a mean of 180 and a standard deviation of 20. What percent of the data is in the interval 140 - 220?
- Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(-e<z<e)=0.2128#, what is #e#?
- The heights of women at a large university are approximately bell-shaped, with a mean of 65 inches and standard deviation of 2.5 inches. What is the probability that two randomly selected women are 65 inches or taller?
- What percentage of the women in the researcher's sample would you expect to have a height of 68.5 inches or less?
- A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .03 significance level. What is the p-value?
- Human body temperatures are normally distributed with a mean of 98.6 and a standard deviation of 0.72.? How do I Find the temperature that separates the top 7% from the bottom 93%?
- How do you find the area under the standard normal distribution curve between z = 0 and z = 0.75?
- How do you find the area under the normal distribution curve to the right of z = –3.24?
- How do you find the area under the normal distribution curve to the right of z = –3.24?
- How do you find the area under the normal distribution curve between z = 1.52 and z = 2.43?
- The time required to finish a test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. What is the z-Score for a student who finishes the test in 45 minutes?