Homework due 3/7/2017
Reading assignment for next class:Sullivan 8.1
Introduction to Statistics Online Edition (free textbook on vf-tropi.com) p299-315
or your own book, the chapters on “Sampling Distributions for the Mean”
Normal Probability
Find the probability that a z-score is between -1.5 and 2 P(-1.5 ≤ z ≤ 2)
Press 2nd VARS [DISTR]
Scroll down to2:normalcdf(
Press ENTER
It will say:normalcdf(
Type: -1.5,2)
Press ENTER
Answer: 0.91044
What is the probability of getting a z-score value between
1) –0.5 and 3
2) –2.5 and –1.5
Find the probability of getting a z-score
3) below 1.3
4) above–2.3 (draw the picture… then be sneaky…)
For normal distributions that are not standardized:
5) Adult IQs are normally distributed with µ = 100 and σ = 15.
Find the probability that a randomly selected IQ is less than 112.
Press 2nd VARS [DISTR]
Scroll down to2:normalcdf(
Press ENTER
It will say:normalcdf(
Type: –9999,112,100,15)
Press ENTER
Answer:
6) Find the probability that a randomly selected IQ is at least 122: P(x ≥ 122).
You’ll need to type: 122,9999,100,15)
7) Find the probability that a randomly selected IQ is between 112 and 122:
P(112 ≤ x ≤ 122).
You’ll need to type: 112,122,100,15)
So, here’s the pattern for 2:normalcdf
The first number is the lower limit you’re interested in finding (use –9999 for –∞)
The second number is the upper limityou’re interested in finding (use 9999 for ∞)
The third number is the mean (not needed for z-scores)
The fourth number is the standard deviation (not needed for z-scores)
8) Find the z-score for an area of 0.25 to the left of the z-score.
Press 2nd VARS [DISTR]
Scroll down to3:invNorm
Press ENTER
It will say:invNorm(
Type: .25)
Press ENTER
Answer:
The pattern for 2:normcdf: normalcdf(smaller, larger, µ, σ)
2:normalcdf gives the PROBABILITY
The pattern for 3:invNorm: invNorm(area to left of desired z)
3:invNorm gives the z-score value
9) Scores on a particular test are normally distributed with a standard deviation of 4 and
a mean of 30. What is the probability of anyone scoring less than 40?
10) Annual salaries for a large company are approximately normally distributed with a
mean of $50,000 and a of $20,000. What percentage of company workers earn
under $40,000?
11) The amount of time a student taking statistics spends on studying for a test is
normally distributed. If the average time spent studying is 12 hours and the
standard deviation is 4 hours, what is the probability that a student will spend more
than 8 hours studying?
12) The amount of candy dispensed by a candy machine is normally distributed with a
mean of 0.9 oz. and a standard deviation of 0.1 ounces. If the machine is used 500
times, how many times will it dispense more than 1 oz. of candy?