Normal Distribution and Probability

A test score distribution is normal with mean 70 and standard deviation 10. Find the z-score for a student who scored 85.

The heights of a group of plants are normally distributed with mean 24 cm and standard deviation 3 cm. Find the z-score for a plant that is 18 cm tall.

In a normal distribution, about what percent of data lies within 1 standard deviation of the mean?

In a normal distribution, about what percent of data lies between 2 standard deviations below the mean and 2 standard deviations above the mean?

A normal distribution has mean 50 and standard deviation 8. What raw score corresponds to a z-score of 1.25?

A set of SAT practice scores is normally distributed with mean 500 and standard deviation 100. Using the empirical rule, estimate the probability that a randomly selected score is between 400 and 600.

A normal distribution has mean 30 and standard deviation 5. Using the empirical rule, estimate the probability that a value is greater than 40.

The weights of boxes are normally distributed with mean 12 pounds and standard deviation 1.5 pounds. Find the z-score for a box weighing 13.5 pounds.

A normal distribution has mean 100 and standard deviation 15. Using the empirical rule, estimate the probability that a value is less than 85.

A data set is normal with mean 200 and standard deviation 20. What interval contains about 99.7 percent of the data?

The time it takes students to finish a quiz is normally distributed with mean 30 minutes and standard deviation 4 minutes. Estimate the probability that a student takes between 26 and 34 minutes.

A normal distribution has mean 75 and standard deviation 5. Find the raw score that is 2 standard deviations below the mean.

A standardized exam has scores that are normally distributed with mean 600 and standard deviation 80. Find the z-score for a score of 520.

A normal distribution has mean 40 and standard deviation 6. Using the empirical rule, estimate the probability that a value is between 34 and 52.

The diameters of machine-made bolts are normally distributed with mean 10 mm and standard deviation 0.2 mm. Using the empirical rule, estimate the probability that a bolt has a diameter between 9.8 mm and 10.2 mm.