Stats test 2

35. Circuit boards for wireless telephones are etched, in an acid bath, in batches of 100 boards. A sample of seven boards is randomly selected from each lot for inspection. A particular batch contains two defective boards; and x is the number of defective boards in the sample. P(x=2) is _______. a) 0.1315 b) 0.8642 c) 0.0042 d) 0.6134 e) 0.0034

(2 (98 2) 5) __________ (100 7)

Suppose you are working with a data set that is normally distributed with a mean of 400 and a standard deviation of 20. Determine the value of x such that 60% of the values are greater than x. a) 404.5 b) 395.5 c) 405.0 d) 395.0 e) 415.0

395.0 Ask for help

16. Suppose the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140, inclusively (90 x 140), then the height of this distribution, f(x), is __________________. a) 1/90 b) 1/50 c) 1/140 d) 1/200 e) 1/500

HIGTH DISTRIBUTION 1 ------- B-A 1 -------- 140- 90 b) 1/50

17. If the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140, then the mean of this distribution is __________________. a) 115 b) 230 c) 45 d) 70 e) unknown

MEAN DISTRIBUTION B+A -------- 2 140 + 90 _________ 2 a) 115

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x<2) is ______________. a) 0.3370 b) 0.9853 c) 0.9785 d) 0.2333 e) 0.5000

OUT OF THE 2000 NAME 40 PERCENT ARE BAD. 40 PERCENT OF 2000 IS 800 P(X<2) = P (X=0) + P(X = 1) (800 (1200 (800 (1200 0) 5) 1) 4) --------------------- +--------------------- (2000 (2000 5) 5) MATH PROBABILITY 3 a) 0.3370

If x is uniformly distributed over the interval 8 to 12, then the probability, P(10.0 < x< 11.5), is __________________. a) 0.250 b) 0.333 c) 0.375 d) 0.500 e) 0.750

P (10 <X<11.5) = REMEMBER PROBABILITY IS ON TOP BIG TO SMALL 11.5 -10 -------------- 12 - 8 c) 0.375

A Poisson distribution is characterized by one parameter.

T

25. A z score is the number of __________ that a value is from the mean. a) variances b) standard deviations c) units d) miles e) minutes

b) standard deviations

If x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4? a) .0055 b) .0063 c) .124 d) .232 e) .994

probability that x is equal to ( A GIVEN NUMBER) ---- USE CALCULATOR 2ND VARS BINOMIAL PDF N, P , (GIVEN NUMBER) a) .0055

24 A market research team compiled the following discrete probability distribution for families residing in Randolph County. In this distribution, x represents the number of evenings the family dines outside their home during a week. x P(x) 0 0.30 1 0.50 2 0.10 3 0.10 The mean (average) value of x is _______________. a) 1.0 b) 1.5 c) 2.0 d) 2.5 e) 3.0

a) 1.0 O.30 X 0 + 1 X .50 +2 X .10 +3 X .10

24. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z < -2.1)? a) 0.4821 b) -0.4821 c) 0.9821 d) 0.0179 e) -0.0179

d) 0.0179

Let z be a normal random variable with mean 0 and standard deviation 1. What is P(1.3 < z < 2.3)? a) 0.4032 b) 0.9032 c) 0.4893 d) 0.0861 e) 0.0086

d) 0.0861

The area to the left of the mean in standard normal distribution is equal to _______. a) the mean b) 1 c) the variance d) 0.5 e) -0.5

d) 0.5

21. The hypergeometric distribution must be used instead of the binomial distribution when ______ a) sampling is done with replacement b) sampling is done without replacement c) n≥5% N d) both b and c e) there are more than two possible outcomes

d) both b and c

The net profit from a certain investment is normally distributed with a mean of $2,500 and a standard deviation of $1,000.. The probability that the investor's net gain will be at least $2,000 is _____________. a) 0.62173 b) 0.34133 c) 0.04328 d) 0.30854 e) 0.69146

e) 0.69146

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women. The probability that all three faculty selected are men is approximately _______ a) 0.05 b) 0.33 c) 0.11 d) 0.80 e) 0.90

they want 3 boys of the 4 and 0 of the 5 girls there are a total of 9 people and they was 3 of them (4 (5 3) 0) ------------- ( 9 3) a) 0.05

To compute the variance of a discrete distribution, it is not necessary to know the mean of the distribution.

F

Variables which take on values only at certain points over a given interval are called continuous random variables.

F

22. On Monday mornings, customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen minute interval. Using the Poisson distribution, the probability that five cars will arrive during the next five minute interval is _____________. a) 0.1008 b) 0.0361 c) 0.1339 d) 0.1606 e) 0.3610

Customer arrive at the coffee shop at rate of 6 cars per 15 mins, implies, in 1 min 6/15 cars and in 5 mins (6/15)*5 = 2 cars. So your lamba = 2 , ( 2 cars per 5 mins) b) 0.0361 P(X=5) = e^(-2). 2^5 / 5! = 0.0361.

26. If x is a binomial random variable with n=10 and p=0.8, the mean value of x is _____. a) 6 b) 4.8 c) 3.2 d) 8 e) 48

E ( x) = N X P 10 X .8 = 8 d) 8

A normal distribution with a mean of zero and a standard deviation of 1 is called a null distribution.

F

A normal variable can be transformed to standard normal variable by J-transformation.

F

A standard normal distribution has a mean of one and a standard deviation of one.

F

A variable that can take on values at any point over a given interval is called a discrete random variable

F

Both the Poisson and the binomial distributions are discrete distributions and both have a given number of trials.

F

For a binomial distribution in which the probability of success is p = 0.5, the variance is twice the mean.

F

For every random variable, both discrete and continuous, P (a ≤ x ≤ b) = P (a < x < b)

F

For the Poisson distribution the mean represents twice the value of the standard deviation.

F

If X~ Binomial (n=20, p=0.2), P(X= 2.5) = 0.35.

F

If X~Uniform (0,1) , mean is equal to 1.

F

In a binomial distribution, p, the probability of getting a successful outcome on any single trial, increases proportionately with every success.

F

In a standard normal distribution, if the area under curve to the right of a z-value is 0.10, then the area to the left of the same z-value is -0.10.

F

Since a normal distribution curve extends from minus infinity to plus infinity, the area under the curve is infinity.

F

The density curve of normal distribution is asymmetrical.

F

The distribution of all values of a random variable is called a normal distribution.

F

The domain/range of a Binomial random variable X can be infinite.

F

The height of the rectangle depicting a uniform distribution is the probability of each outcome and it same for all of the possible outcomes.

F

The number of successes in a hypergeometric distribution is unknown

F

The probability of success is equal to probability of failure for every trial in Binomial distribution.

F

If x is uniformly distributed over the interval 8 to 12, inclusively (8< x< 12), then P(x> 10) is __________________. a) 0.750 b) 0.000 c) 0.333 d) 0.500 e) 0.900

P(X >10) 10 IS GREATER THEN 8 SO IT KNOCKS IT OUT 12-10 _________ 12-8 d) 0.500

31. For the same problem question 30. , P(x>0) is ______________. a) 0.2172 b) 0.9533 c) 0.1846 d) 0.9222 e) 1.0000

P(X<0) = 1 - P(X=0) d) 0.9222

A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses no questions? a) 0.000 b) 0.200 c) 0.500 d) 0.031 e) 1.000

PERCENT CHANCE RAISED TO THE NUMBER OF PROBLEMS (.5)^ 5 d) 0.031

27. If x is a binomial random variable with n=10 and p=0.8, the standard deviation of x is _________. a) 8.0 b) 1.26 c) 1.60 d) 64.0 e) 10

SD Square rood of N X P (1-P) SQUARE ROOD OF 10 X .8 (1 - .8) b) 1.26

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 5 cars arriving over a five-minute interval is _______. a) 0.0940 b) 0.0417 c) 0.1500 d) 0.1008 e) 0.2890

SO THEY ARE LOOKING FOR HOW MANY CARS WILL HAPPEN IN 5 MINUTES P (X=5) 3 IS THE NUMBER OF CARS 5 IS THE AMOUNT OF TIME e^-3 (3) ^5 _____________ 5 ! d) 0.1008

If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 x 30), then the standard deviation of this distribution is __________________. a) unknown b) 8.33 c) 0.833 d) 2.89 e) 1.89

STANDARD DEVIATION OF A DISTRIBUTION B-A ________ SQUARE ROOD OF 12 30 - 20 = 10 / SQUARE ROOD OF 12 d) 2.89

25. From problem 24. The standard deviation of x is _______________. a) 1.00 b) 2.00 c) 0.80 d) 0.89 e) 1.09

SUM (X-M) ^2 P (X) X 0^2 = 0 1^2=1 X (.5) = .5 2^2=4 X (.1) = .4 3^2=9 X (.1) = .9 + ___________ =1.8 -1 =.8 Square root of .8 = .89 d) 0.89

A random variable is continuous if its possible values are all points in some interval.

T

A uniform continuous distribution is also referred to as a rectangular distribution.

T

As in a binomial distribution, each trial of a hypergeometric distribution results in one of two mutually exclusive outcomes, i.e., either a success or a failure.

T

For a continuous random variable x, the area under the density curve within an interval a to b represents the probability that the value of x is between a and b.

T

In a binomial experiment, any single trial contains only two possible outcomes and successive trials are independent.

T

In a hypergeometric distribution the population, N, is finite and known.

T

Normal distribution is a symmetrical distribution with its tails extending to infinity on either side of the mean.

T

Normal distribution is used in inferential statistics.

T

The Poisson distribution is best suited to describe occurrences of rare events in a situation where each occurrence is independent of the other occurrences.

T

The amount of time a patient waits in a doctor's office is an example of a continuous random variable

T

The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

T

The number of finance majors within the School of Business is an example of discrete random variable.

T

Which of the following conditions is not a condition for the hypergeometric distribution? a) the probability of success is the same on each trial b) sampling is done without replacement c) there are only two possible outcomes d) trials are dependent e) n < 5%N

a) the probability of success is the same on each trial e) n < 5%N

If the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140, inclusively (90 x 140), then P(x = exactly 100) is __________________. a) 0.750 b) 0.000 c) 0.333 d) 0.500 e) 0.900

b) 0.000

30. If X ~ Normal ( 15, 5), P ( X < 5.25) a) 0.02619 b) 0.02559 c) 0.02500 d) 0.02442 e) 0.02680

b) 0.02559

The probability of selecting 3 female employees and 7 male employees to win a promotional trip a company with 10 female and 50 male employees would best be modeled with the _______. a) binomial distribution b) hypergeometric distribution c) Poisson distribution d) hyperbinomial distribution e) exponential distribution

b) hypergeometric distribution

28. If X ~ Normal ( 15, 5), P ( X > 7.25 ) a) 0.06057 b) 0.35213 c) 0.93943 d) 0.05000 e) 0.00000

c) 0.93943

23. The volume of liquid in an unopened 1-gallon can of paint is an example of _________. a) the binomial distribution b) both discrete and continuous variable c) a continuous random variable d) a discrete random variable e) a constant

c) a continuous random variable