STA 13

The probability of an impossible event

0

Find the indicated complement. 15)The probability that Luis will pass his statistics test is 0.58. Find the probability that he will fail his statistics test.

0.42

the probability of an event

0<P(A)<1

The the probability of a certain event

1

P(A) + P( complement of A) = 1

1 - P(A) = P( complement of A) 1 - P( complement of A) = P(A)

Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual.Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. 10)A body temperature of 99.5° F given that human body temperatures have a mean of 98.20° F and a standard deviation of 0.62°.

2.1; unusual

Find and indicate the probability 14)A die with 8 sides is rolled. What is the probability of rolling a number less than 7?

3/4

Find the indicated measure. 12)The weights (in pounds) of 30 newborn babies are listed below. Find Q 1. 5.5 5.7 5.8 6.0 6.1 6.1 6.3 6.4 6.5 6.6 6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.27.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7

6.4 lbs

Empirical Rule

68 (34/34), 95 (34 + 13.5 / 34 + 13.5) 97.5 (34 + 13.5 + 2.35 / 34 + 13.5 + 2.35)

Determine which score corresponds to the higher relative position. 11)Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150?

A score of 92

A company advertises an average of 42,000 miles for one of its new tires. In the manufacturing process there is some variation around that average. Would the company want a process that provides a large or a small variance? Justify your answer.

A small variance is preferred, since this measure denotes consistency in the lifetime of the tires. Given small variation, buyers would get useful mileage from those tires around 42,000. Large variation would indicate that some buyers could have their tires wear out many miles short of 42,000, whereas others might get good use out of many miles past 42,000

We want to compare two different groups of students, students taking Composition 1 in a traditional lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation?

By knowing the standard deviation for both groups, we would have an idea about how the individual scores for each group varied about 85. The smaller standard deviation would indicate that individual scores were closer to 85 than would a larger standard deviation

13)Suppose that all the values in a data set are converted to z-scores. Which of the statements below is true? A: The mean of the z-scores will be zero, and the standard deviation of the z-scores will be the same as the standard deviation of the original data values. B: The mean and standard deviation of the z-scores will be the same as the mean and standard deviation of the original data values. C: The mean of the z-scores will be 0, and the standard deviation of the z-scores will be 1. D: The mean and the standard deviation of the z-scores will both be zero.

C : The mean of the z-scores will be 0, and the standard deviation of the z-scores will be 1.

A comparison is made between summer electric bills of those who have central air and those who have window units. May June July Aug Sept Central $32 $64 $80 $90 $65 Window $15 $84 $99 $120 $40

Central air: mean = $66.20 median = $65 Window unit: mean = $71.60 median = $84 Window units appear to be significantly more expensive

Central Limit Theorem (CLT)

For non-normal populations, the distribution of the sample means (x̄) will be approximately Normal for a large n : (n>30)

The data set below consists of the scores of 15 students on a quiz. For this data set, which measure of variation do you think is more appropriate, the range or the standard deviation? Explain your thinking. 90 90 91 91 89 90 89 91 91 90 60 90 89 90 91

For this data set, the range is very misleading. The range depends only on the smallest and largest values and the remainder of the data contributes nothing to the range. In this case, the smallest value is an outlier. Thus even though all the values except one lie between 89 and 91, the range is 31. The standard deviation, while it will also be affected by the outlier, will be less misleading, as it depends on every piece of data.

Histograms and Bar graphs are both bar charts. What is the significant difference between the two?

Histograms convey quantitative information about shapes of distributions. Pareto charts convey comparative information about relative standing of categorical data.

Marla scored 85% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the85 percentile in mathematics. Explain the difference in these two scores.

Marla's score of 85% on her statistics exam tells us that Marla knew 85% of the content on that exam. Marla's percentile score of 85 tells us that her score was better than 85% of the scores of examinees on that test.

Finding the P(-1 < z < 2)

P( z < 2) - P(z < -1) find these values on the side of the chart then look for there Z score values within the chart

what does Central Limit Theorem tell us about the sampling distribution fo the sampling mean?

The distribution of the sample mean. 1) the population mean = the sample mean the sample standard deviation = (Populations SD/ the square root of the sample size) 2) If X is non-normal ( X follows another distribution) If n > 30, Sample mean ~ Normal ( sample mean, (SD/ square root of sample size))

Are sample means a good estimator of the population mean?

Yes! Sample means are unbiased and do not systematically underestimate or overestimate the true population mean.

statistic

a numerical measurement describing some characteristic of a sample

qualitative data

can be separated into categories that are distinguished by nonnumeric characteristics

quantitative data

consist of numbers representing counts or measurements

parameter

is a numerical measurement describing some characteristic of a population

sample

is a subset of elements drawn from the population

census

is the collection of data from every element of the population

Population

is the complete collection of all elements

discrete data

result from either a finite number of possible values or a countable number of possible values

continuous numerical data

result from infinitely many possible values that can be associated with points on a continuous scale so that there are no gaps or interruptions.

if given the z score, where do you find the point at?

you look for the given z score in the table then follow it to the edges to give you the point.

z score formula

z = (x - μ)/σ