MAT 274 Midterm Review

criteria for a probability distribution

-values for x must be numerical -probabilities must be between 0 and 1 -do the probabilities add up to 1

simple random sample

A sample of size n selected from the population in such a way that each possible sample of size n has an equal chance of being selected.

in a standard normal deviation...

STDEV: 1 mean: 0

central limit theorem

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

random sample

all members of the population are equally likely to be chosen

Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If one order is selected, find the probability of getting an order that is not accurate or is from Rest C. Are the events of selecting an order that is not accurate and selecting an order from Rest C disjoint events.

answer: -The prob of getting an order from Rest C or an order that is not accurate is: .326 -the events (are not) disjoint because it (is) possible to (receive an inaccurate order from Rest C) how to solve: -find total - find P(not accurate): not accurate/total -find P (from rest C) from rest c/total -find P (not accurate and from rest C simultaneously): from both/total -answer: P(not accurate) + P(from rest C) - P(simultaneous)

for a data set of chest sizes (distance around chest in in) and weights (lbs) of eight anesthetized bears that were measured, the linear correlation coefficient is r=0.559. Use the table available below to find the critical values or r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation?

answer: -critical values: -7.07, 7.07 -since the correlation coefficient r is (between the critical values), there (is not) sufficient evidence to support the claim of the linear correlation. how to solve: -take into account the # of bears (8) -look at the table for the critical value that matches 8 -write both the positive and negative version of the critical value (comma separated) -if the coefficient is between the critical values then there is not enough evidence to support a linear correlation

Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a self-driving vehicle. Determine whether a prob distribution is given. If a prob distribution is given, find its mean and STDEV. If not a prob distribution, identify the requirement why.

answer: -mean of the random variable: 0.9 adults -the STDEV of the random variable: 0.8 how to solve: -check criteria to meet probability distribution

Use the body temperatures in degrees fahrenheit, listed in the accompanying table. The range of the data is 3.1°F. Use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the actual standard deviation of the data rounded to 2 decimal places, 0.68°F, assuming the standard deviation is within 0.2°F.

answer: -the estimated STDEV is (.78)°F -The estimated STDEV is (within 0.2° of) the actual STDEV. Thus, the estimated STDEV (meets) the goal. how to solve: -take the range and divide by 4 -compare to STDEV (must be within 0.2°F)

The sample space listing the eight simple events that are possible when a couple has three children is​ {bbb, bbg,​ bgb, bgg,​ gbb, gbg,​ ggb, ggg}. After identifying the sample space for a couple having four​ children, find the probability of getting four girls and no boys (in any order).

answer: .0625 how to solve: list all the possible combinations of siblings then find how many of them include four girls and then divide that by the total number

For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 34 beats per min, the mean of the listed pulse rates is x= 77.0 beats per min, and their STDEV is s= 24.7 beats per min.

answer: a. the diff is (-43) beats per min b. the diff is (-1.74) standard deviations c. the z score is z= 1.74 d. the lowest pulse rate is (not significant) how to solve: a. lowest-mean (based on which is phrased first) b. take your difference and divide by the standard deviation (make it positive!) c. z score is the same as the previous answer d. look at criteria for significance

When playing roulette at a casino, a gambler is trying to decide whether to bet $10 that the outcome is any one of the five possibilities 00, 0, 1, 2, or 3. The gambler knows that the expected value of the $10 bet for a single number is -$1.06. For the $10 bet that the outcome is 00, 0, 1, 2 or 3, there is a prob of 5/38 of making a net profit of $6 and a 33/38 prob of losing $10.

answer: -expected value: -0.79 -since the expected value for the bet on the number 32 is (less) than the expected value for the bet that the outcome is 00, 0, 1, 2, or 3, the bet on 00, 0, 1, 2, or 3 is better. how to solve: -make a table where x is the profit and loss -P(x) is the associated probs solved -make another column that multiples x and P(x) -the expected value is the sum of the last column -b. base the higher or lower on the single # $value (1.06 is lower than our mean) -b. less bad is better gamble

Assume that hybridization experiments are conducted with peas having the property that for​ offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 14. Complete parts​ (a) through​ (c) below. a) The value of the mean is u=_____. The value of the standard deviation is o=_____. b) Values of _____ peas or fewer are significantly low. Values of _____ peas or greater are significantly high. c) The result _____ significantly low, because 8 peas with green pods is __________ _____ peas.

answers: 10.5 a. 1.6 b. 7.3 13.7 c. the result (is) sig low, because 1 pea with green pods is (less than) (7.3) how to solve: check excel (11) use binomial calc

Refer to the figure below in which surge protectors p and q are used to protect an expensive high-definition television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.96 probability of working correctly when a voltage surge occurs.

answers: a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the TV? 0.9984 b. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the TV? 0.9216 c. The series arrangement provides better protection because it has a higher probability of protection how to solve: -write out the probability that both surge 1 and surge 2 works -write out the probability that each do not work (1-corresponding) -find the prob it is damaged by multiplying the 2 probs that it wont work -find the prob that it wont be damaged (1-prob damaged) -for undamaged parallel multiply the prob that both work

Assume that thermometer readings are normally distributed with a mean of 0°C and a standard dev of 1°C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the prob of the reading. Between 1.50 and 2.25

how to solve: -put each value in the normal calc and then paste the highest value's left prob into the left P High and the lowest value's left prob into the Left P low -the area in between is the prob

STDEV cannot be

negative

disjoint

never occur at the same time

range rule of thumb

stdev is approximately the range/4

b. For the same class described in part​ (a), the 36 student names are written on 36 individual index cards. The cards are shuffled and six names are drawn from the top.

the sample is a simple random sample. it is a random sample

a. A statistics class with 36 students is arranged so that there are 6 rows with 6 students in each​ row, and the rows are numbered from 1 through 6. A die is rolled and a sample consists of all students in the row corresponding to the outcome of the die.

this sample is not a simple random sample. It is a random sample

c. For the same class described in part​ (a), the six youngest students are selected.

this sample is not a simple random sample. it is not a random sample