Data Distributions
Find the area under the standard normal curve to the left of z=−2.53 and to the right of z=−0.58.
0.0057+0.7190= 0.7247
Find the area under the standard normal curve to the left of z=1.56. Round your answer to four decimal places, if necessary.
0.9406
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 520 hours. Find the probability of a bulb lasting for at most 554 hours. Round your answer to four decimal places.
554-520/15=2.27 Find 2.27 in the table provided 0.9884
Given X=72.8, μ=66.5, and σ=3.5, indicate on the curve where the given X value would be.
72.8
continuous random variable
A continuous random variable is a random variable that can assume any value on a continuous segment(s) of the real number line.
discrete random variable
A discrete random variable is a random variable which has a countable number of possible outcomes.
Point Estimator
A point estimator is a single-valued estimate, calculated from the sample data, which is intended to be close to the true population value.
Biased
A sample is biased if it over represents or under represents some segment(s) of the population.
Identify the sampling technique used for the following study. Include each member of the entire sampling frame.
Census
Identify the sampling technique used for the following study. A pollster interviews each member from each of the fifteen randomly chosen neighborhoods throughout a city.
Cluster Sampling
Identify the sampling technique used for the following study. A statistics student interviews each member from each of the five randomly chosen zoning districts in a town.
Cluster Sampling
Unbiased
If the average value of an estimator equals the population parameter being estimated, the estimator is said to be unbiased.
For a quantitative variable in a particular population, how many different sample means are there?
Many
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.06 If 333 are sampled, what is the probability that the sample proportion will be less than 0.03? Round your answer to four decimal places.
Mean: 0.06 SD: √(0.06)(1−0.06)/333≈0.013 Below: 0.03
Suppose the horses in a large stable have a mean weight of 1467lbs, and a standard deviation of 93lbs. What is the probability that the mean weight of the sample of horses would be less than 1477lbs if 49 horses are sampled at random from the stable? Round your answer to four decimal places.
Mean: 1467 Standard Deviation: 93/√49= 13.28571 Below: 1477 =0.7742
Which plan has the least amount of risk? Plan A Payout P(payout) $30,000 0.59 $35,000 0.09 $85,000 0.32 Plan B Payout P(payout) -$10,000 0.13 $5,000 0.21 $60,000 0.66
Plan A
Consider the following data: X: 6, 7, 8, 9, 10 P(X=x): 0.1, 0.3, 0.1, 0.1, 0.4 Step 1 of 5 : Find the expected value E(X). Round your answer to one decimal place. Step 2 of 5 : Find the variance. Round your answer to one decimal place. Step 3 of 5 : Find the standard deviation. Round your answer to one decimal place. Step 4 of 5 : Find the value of P(X<9). Round your answer to one decimal place. Step 5 of 5 : Find the value of P(X>7). Round your answer to one decimal place.
Step 1: 6*0.1=0.6 7*0.3= 2.1 8*0.1= 0.8 9*0.1= 0.9 10*0.4= 4 Add sum = 8.4 Step 2: 6^2*0.1= 3.6 7^2*0.3= 14.7 8^2*0.1= 6.4 9^2*0.1= 8.1 10^2*0.4= 40 =2.25 (use Excel sheet) Step 3: 1.49 Step 4: We need to find P(X<9). In order to find this probability, we must add the probabilities of any values of x that are less than 99. Enter the indicated probabilities in the boxes below. 0.1+0.3+0.1=0.5 Step 5: 0.1+0.1+0.4=0.6
Identify the sampling technique used for the following study. A statistics student interviews every other member from the entire sampling frame.
Systematic Sampling
dentify the sampling technique used for the following study. A scientist interviews every tenth member from the entire sampling frame.
Systematic Sampling
Find the expected value E(X) of the following data. Round your answer to one decimal place. X: 4, 5, 6, 7, 8 P(X=x): 0.1, 0.1, 0.2, 0.2, 0.4
The first step in finding this sum is to multiply each value of x by the probability that this value will occur. Find the indicated product and enter your answer in the box below. 4*0.1= 0.4 5*0.1= 0.5 6*0.2= 1.2 7*0.2= 1.4 8*0.4= 3.2 Next add the sum: 0.4+0.5+1.2+1.4+3.2= 6.7 6.7
Which of the following is a good point estimator for the population standard deviation?
s
Which of the following is a good point estimator for the population variance?
s^2
Find the area under the standard normal curve to the left of z=−0.7. Round your answer to four decimal places, if necessary.
0.242
Find the area under the standard normal curve between z=−2.97 and z=2.67. Round your answer to four decimal places, if necessary.
0.9962−0.0015= 0.9947
A soft drink machine outputs a mean of 29 ounces per cup. The machine's output is normally distributed with a standard deviation of 4 ounces. What is the probability of filling a cup between 34 and 35 ounces? Round your answer to four decimal places
35-29/4= 1.5 34-29/4=1.25 0.9332-0.8944= 0.0388
Sampling Frame
A sampling frame is a list which identifies all members of the population.
Simple Random Sample
A simple random sample from a finite population is one in which every possible sample of the same size n has the same probability of being selected.
Select the scenario which is an example of simple random sampling.
College administration wants to conduct a survey to determine the demand for an insurance program at the college. Students are selected randomly from the college and mailed a questioner.
Classify the following as either a discrete random variable or a continuous random variable. The amount of sugar imported by the U.S. in a day.
Continuous
Classify the following as either a discrete random variable or a continuous random variable. The amount of water (in gallons) used daily in a home.
Continuous
Classify the following as either a discrete random variable or a continuous random variable. The highway miles per gallon for an automobile.
Continuous
Classify the following as either a discrete random variable or a continuous random variable. The weights of 89 newborn babies at a local hospital.
Continuous
Identify the sampling technique used for the following study. A market researcher interviews the first fifty members to arrive.
Convenience Sampling
Identify the sampling technique used for the following study. A statistics student interviews the last fifteen students to leave.
Convenience Sampling
Classify the following as either a discrete random variable or a continuous random variable. Birth years of members of your family.
Discrete
Classify the following as either a discrete random variable or a continuous random variable. The heartbeats per minute of 64 randomly selected people.
Discrete
Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not. X: -5, 6, 8 P(X=x): 1/8, 3/8, 1/2
First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision. YES Since the probabilities lie inclusively between 0 and 1 and the sum of the probabilities is equal to 1.
The mean cost of a five pound bag of shrimp is 40 dollars with a standard deviation of 7 dollars. If a sample of 51 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 40.6 dollars? Round your answer to four decimal places
Mean: 40 Standard Deviation: 7/√51= 0.980196 Below: 40.6 =0.7298
The mean lifetime of a tire is 46 months with a variance of 49. If 133 tires are sampled, what is the probability that the mean of the sample would be greater than 47.05 months? Round your answer to four decimal places.
Mean: 46 SD: √49= 7 7/√133=0.606976 Above: 47.05 =0.0418
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 77 minutes with a mean life of 551 minutes. If the claim is true, in a sample of 135 batteries, what is the probability that the mean battery life would be greater than 545.6 minutes? Round your answer to four decimal places.
Mean: 551 Standard Deviation: 77 77/√135 ≈6.627105 N: 135 (sample size) 545.6-551/6.627105= -0.81 =0.7924
Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Spinning an American roulette wheel 82 times and recording the number the ball lands on.
No, there are more than two possible outcomes on each trial of the experiment.
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X=6), n=7, p=0.4
Number of trial= 7 p= 0.4 Number of success (x)= 6 Probability of x successes - P(x) 0.01720
Suppose 52% of politicians are lawyers. If a random sample of size 416 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 53%? Round your answer to four decimal places.
Sample Size: 416 Number of successes: 0.52*416= 216 (rounded) x= 0.53 =0.66990 ROUND= 0.6610
Select the scenario which is an example of voluntary sampling.
The music festival gives out a People's Choice Award. To vote a participant just texts their choice to the festival sponsor.
Sampling Distribution of a Statistic
The sampling distribution of a statistic (such as the sample mean or sample proportion) is the probability distribution of all values of the statistic when all possible samples of size n are taken from a population.
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.04. If 222 are sampled, what is the probability that the sample proportion will be less than 0.05? Round your answer to four decimal places.
USE EXCEL =0.7765
A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 3 insects will die? Round your answer to four decimal places.
X=number of insects killed by the insecticide= 3 p=probability that insects will die=60%=0.6 n=total number of insects=7 Probability of x successes - P(x)= 0.1935
A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 2 insects will survive?
X=number of insects not killed by the insecticide= 2 p=probability that insects will survive=100%−60%=40%=0.4 n=total number of insects=7
Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Spinning an American roulette wheel 30 times and recording the number of times the ball lands on red.
Yes
