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Chapter 2 – Calculator Worksheet
Name: __________________________
All of the areas under normal curves can be found using the TI graphing calculators. The two functions you want to know are normalcdf (which calculates the areas under normal curves) and invnorm (which calculates the values of a normal distribution which has a specified area to the left of it). The information needed for a standard normal distribution: Normalcdf( left z-score, right z-score) Invnorm( area to the left of the point in question) Outputs a z-score These can also work with any normal distribution: Normalcdf( left value, right value, mean, standard deviation) Invnorm( area to the left of a point, mean, standard deviation) Outputs the actual value of that point Even if you are going to use these functions, you MUST draw, label, and shade a normal curve and show any calculations that would be necessary when using the chart. 1. Find the area under the standard normal curve that lies… a. To the left of z = 0.85
d. To the right of z = -0.67
b. To the left of z = -0.98
e. Between z = .12 and z = 2.76
c. To the right of z = 1.23
f. Between z = -1.75 and z = 0.55
2. Find z with… a. 35% of observations falling below it
b. 15% of observations falling above it
3. The weights of 10-week-old (domestic) kittens are normally distributed with a mean of 24.5 ounces and a standard deviation of 5 ounces. a. What proportion of 10-week-old kittens will weigh less than 14 ounces?
b. What proportion of 10-week-old kittens will weigh more than 33 ounces?
c. What proportion of 10-week-old kittens will weigh between 14 and 33 ounces?
d. A kitten whose weight is in the bottom 10% of weights is called undernourished. What is the cutoff point for the weight of an undernourished kitten?
4. Which of the following situations are unknown percentage problems and which are unknown value problems? For each, draw and label a normal curve, showing the three quantities that are given and the one quantity to find. a. In a recent year, students entering the University of Florida had a mean SAT I score of 1135, with a standard deviation of 180. The distribution was roughly normal. What percentage of SAT I scores were greater than 1300?
b. In 2000, the mean SAT I math score nationally was 514 with a standard deviation of 113. Find the upper quartile of the distribution.
5. In a law school class, the entering students averaged about 30 on the LSAT with a standard deviation of about 8. The histogram of LSAT scores followed the normal curve reasonably well. a. About what percentage of the class scored between 21 and 37?
b. One student was 0.5 standard deviations above average on the LSAT. About what percentage of the students had lower scores than she did?
6. Quick Start Company makes 12-volt batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed with a mean of 45 months and a standard deviation of 8 months. a. If Quick Start guarantees a full refund on any battery that fails within the first 36 months period after purchase, what percentage of its batteries can the company expect to replace?
b. If Quick Start does not want to replace more than 10% of its batteries under the full-refund guarantee policy, for how long should they guarantee the batteries (to the nearest month)?