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Using the Calculator with Normal Curves: 2nd VARS (DISTR) Finding % or area underneath the curve: Normal Cumulative Density Function (normalcdf) Summary: o normalcdf (left bound, right bound) o use ­1000 and 1000 o If not already in standard normal form put mean and standard deviation after bounds: normalcdf (left bound, right bound, mean, sd) ● P(z < z​
) 1​
normalcdf(­1000, z​
) 1​
● P(z > z​
) 1​
normalcdf(z​
, 1000) 1​
● P(z​
<z < z​
) 1​
2​
normalcdf(z​
, z​
) 1​
2​
● P(X < X​
) 1​
normalcdf(­1000, X​
, μ, σ) 1​
● P(X > X​
) 1​
normalcdf(X​
, 1000, μ, σ) 1​
● P(X​
<X < X​
) 1​
2​
normalcdf(X​
, X​
, μ, σ) 1​
2​
Finding z­score: Inverse Normal (invnorm) Summary: o
invnorm (percent or area) o
put it in decimal form o If not already in standard normal form put mean and standard deviation after bounds: invnorm (percent or area, mean, sd) ● standard normal distribution invnorm(area to left) ● normal distribution invnorm(area to left, μ, σ) Normal Curve Calculator Problems: Practice!!!! ☺ 1. The lifetimes of batteries made by a certain company are normally distributed with a mean of 98 hours and a standard deviation of 4.5 hours. a. What percent of batteries will last less than _________ hours? b. If X is the distribution of battery lifetimes, find the relative frequency of X < _____ hours. c. P(X > ________) d. P (_____ < x < ______) e. If a battery lasts longer than _______% of all batteries, how long does the battery last? 2. X = N (12, 4). Find P (X > _____) 3. Find P (Z < _________) 4. X = N (5, .4). Find the percentage of observations that are within 1 standard deviation of the mean. 5. X = N (100, 15). Find P (______ < X < __________) 6. X = N (615, 107). Find the __________percentile. 7. The temperature at any random location in a kiln used in the manufacture of bricks is normally distributed with a mean of 1000 and a standard deviation of 50 F. a. Bricks fired at a temperature above ___________ degrees will crack and be discarded. What proportion of bricks wil crack during the firing process? b. If bricks are below ___________ degrees they will miscolor. What proportion of glazed bricks will miscolor? 8. The distribution of actual weights of 8.0 ounce chocolate bars produced by a certain machine is normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. a. Find P (x < _________) b. What proportion weigh between _______ and ________ ounces? 9. The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the bottom _________ of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? 10. Find P( z < ________) 11. Find P (z > _________) 12. Find P (_______ < z < ________) Challenge Problem #1 We know that s of a distribution is _____. ________% of the distribution is less than ____. Find the mean of the data. a) 4.5
b) 5
c) 5.5 d) 6
e) 6.5 Challenge Problem #2: s = _______. 75% of the data is less than ___________. Find m of this data. Challenge Problem #3: m = ________. 40% of the scores are less than ________. Find s of this distribution. Challenge Problem #4 The third quartile of a distribution of test scores is _________. The scores are normally distributed with m = __________. Find s of this distribution.
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