Statistics and Probability

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In a sample of 162 randomly selected students it was found that the proportion of students planning to travel home for Thanksgiving is 0.73. What is the standard deviation of the sampling distribut...
In a study of the uptake of maternal vaccinations by Indigenous women in Central Australia, 69.6 of the participating women (32 out of 46) received an influenza vaccine while they were pregnant.
After one month's of hard working, the medical student obtained a sample with numerical values (x1,x2,x3,x4) . The sample mean bar{x}_4 = 0.6 . the sample standard deviation is S_4 = 1.0 . a. C...
Find the Z-Score that has 60.3% of it's distribution to the right.
A credit card company has determined that the majority of customers are charging between $200 - $1400 per month. Assume that the monthly charges are uniformly distributed. What is the average amou...
The mean number of births per minute in a country in a recent year was about seven. Find the probability that the number of births in any given minute is: (a) exactly five. (b) at least five. (c)...
The mean test score was 1549 and the standard deviation was 314. Find the z-scores that correspond to each value and determine whether any of the values are unusual. a.) 1940. b.) 1290. c.) 2230. d...
The random variable x represents the number of phone calls an author receives in a day, and it has a Poisson distribution with a mean of 7.8 calls. a. What are the possible values of x ? b. I...
Consider a binomial experiment with n = 12 and p = 0.3 a. Compute f(0) . b.Compute f(10) . c. Compute P(x less than or equal to 1) . d.Compute P(x greater than or equal to 2) . e.. Va...
Find the value of P(X less than -2) . |x| -4| -3| -2| -1| 0 |P(X = x) |0.3 |0.1 |0.2 |0.2 |0.2
X is uniformly distributed between 14 and 23 . What is the Expected value of X ?
If we select 40 rides, what is the probability that at least 10 of those rides were paid in cash? If the probability of being paid in cash is 0.4657743.
A psychologist is collecting data on the time it takes to learn a certain task. For 50 randomly selected adult subjects, the sample mean is 16.40 minutes and the sample standard deviation is 4.00 m...
If the mean is 975 and std dev is 160, what is the cut-off for the bottom 10%? Assume normal distribution.
The probability of a radar station detecting an enemy plane is 0.85. If 4 stations are in use, what is the standard deviation? a. none of these choices. b. 0.71 c. 0.51 d. 1.84 e. 3.40
There are three factors that affect the width of a large-sample confidence interval for p : the confidence interval, the sample size, and the sample proportion, hat{p} . In each of the following...
A survey was taken at a K-6th grade school. Do you have enough time at lunch? Given the table below, answer the following questions. | |Yes |No |Girls |42 |110 |Boys |95 |53...
A sample of 171 random students found that the proportion of students planning to travel home for Thanksgiving is 0.76. What is the standard deviation?
A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are m...
Discussion responses data: | |Yes |No |Girls |42 |110 |Boys |95 |53 a. If b represents the event of selecting a response from a boy, find the complement of b P(b...
The weight of a product is measured in pounds. a sample of 65 units is taken from a recent production. the sample yielded bar{x} = 100 lb, and we know the variance = 100 lb. calculate a 98 p...
When engaging in weight-control (fitness/fat burning) types of exercise, a person is expected to attain about 60% of their maximum heart rate. For 20-year-olds, this rate is approximately 120 bpm....
Find the z-scores that separate the middle 20% of the distribution from the area in the tails of the standard normal distribution. The z-scores are:....
A research group conducted an extensive survey of 3031 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-lo...
If a random variable X follows the discrete uniform distribution U(0, n) , show that Var(X) = dfrac{(n + 1)^2 - 1}{12} .
What are the odds of having a GPA of 3.0 or above given a student is admitted to WMU? | | |GPA 3.0 or above| | | | |yes| no| total | Admitted to WMU|yes| 55| 23| 78 | |no| 7 |15 |22 | |tota...
Which of the following formulas represents the estimator by interval for a normal distribution with the size of a small sample or less than 30 data? a. bar{X} pm Z_{ alpha/2} dfrac{ sigma}{sqrt{n}...
Laura got a bag full of colorful jelly beans. There were 30 of them: 7 orange, 5 green, 3 blue, 4 red, and 11 yellow. After shaking the bag, she randomly selected two jelly beans from the box. Wha...
Based on a poll, 65% of internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among six randomly selected internet users, at le...
A literature professor decides to give a 15-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than...
The X university financial aid office did a study showing that their students spend $980 on average (arithmetic mean) in the college bookstore, with a standard deviation of $138. If a random sampl...
A garment manufacturer knows that the number of flaws per square yard in a particular type of cloth varies with an average of 1.3 per square yard. What is the approximate probability of obtaining...
In a random sample of 7 residents of the state of Montana, the mean waste recycled per person per day was 1.1 pounds with a standard deviation of 0.64 pounds. a. Determine the 90% confidence inter...
The servicing time at the drive-through lane of a fast food restaurant follows an exponential distribution. The average servicing time is 1.5 minutes. a. What is the probability that it takes more...
You know that the average of online campus students is 598 students, with a deviation of 23 students. If you know that they follow a normal distribution, what would be the probability that the next...
The length of incoming calls at the call center of a major telecommunication service provider follows a Normal distribution with an average of 7.5 minutes. The standard deviation of the distributio...
A manufacturer of light bulbs has sampled 40 bulbs in order to determine the population mean life of the bulbs. The sample mean was 1,200 hours with a standard deviation of 100. The manufacturer wo...
Global warming is a concern for this and future generations. Measurements of the earth's atmospheric temperature have been taken over the past 100 years. If the average temperature has been 50 degr...
An inspector correctly identifies defective products 90% of the time.For the next 10 products, the probability that he makes fewer than 2 incorrect inspection is 0.736. True False
Food preparation in a restaurant must be performed carefully to prevent food spoilage or undercooked or overcooked food. Oven temperature is a critical factor. One concerned chef monitors oven temp...
A study from a consumer research company reported that 51% of teenagers sent a text during the past 30 days. A sample of 14 teenagers is studied. Round to 4 decimal places. What is the probability...
The average length of time it takes to complete the exam is 80 minutes with standard deviation 9 minutes. The data is normally distributed. What percentage of the students will complete the exam be...
There are 1000 students in a high school. Among the 1000 students, 250 students take AP Statistics, and 300 students take AP French. 100 students take both AP courses. Let S be the event that a ran...
Assume the weights of men are normally distributed with a mean of 170 lbs and a standard deviation of 30 lbs. (a) Find the 75th percentile for the distribution of men's weights. (b) What is the pr...
If the mean speed on a highway is 59 MPH, and the speed limit is 55 MPH, given a standard deviation of 4 MPH, approximately what percent of people speed on this highway? (Assume a normal distributi...
Twelve (12) out of 1000 randomly selected people were found to be carriers of a particular virus. Find 99% confidence interval for the true percentage of carriers in the population.
Find the z-score having area 0.86 to its right under the standard normal curve.
A political analyst is interested in predicting whether a certain candidate will win an election. In a random sample of 800 likely voters, 412 indicated they would vote for the candidate. a. Use t...
The assets (in billions of dollars) of the four wealthiest people in a particular country are 36, 32, 20, 14. Assume that samples of size 2 are randomly selected with replacement from this populati...
P( X) = x/15 Represent a probability distribution for x= 1, 2, 3, 4 ,5.
If the probability distribution of X is: X P(X) 3 1/8 4 1/8 5 3/8 6 3/8 What is the expected value of X?
Given N(1,900, 500), out of 2,000 students who took the SAT test in June 2015, about how many of them would expect a score greater than 2,250?
A patient recently diagnosed with all Alzheimer's disease takes a cognitive abilities test and scores 45. The name on this test is 52 and a standard deviation is 5. What is the patients percentile...
The animal colony at a hospital contains 12 male rats and 18 female rats. Of the 18 females, 15 are white and 3 spotted. Of the 12 males, 6 are white, and 6 are spotted. Suppose that you randomly s...
A fifth grader take a standardized achievement test ( mean = 125, standard deviation = 15) and scores a 148. What's is the child's percentile rank?
The average length of time it takes to the complete exam is 80 minutes with standard deviation 9 minutes. The data is normally distributed. The instructor wants the exam to be long enough so that 9...
It is known that 25% of pairs of jeans at a large warehouse are defective. A random sample of 36 pairs of jeans is selected. Find the probability that less than 20% of them are defective. (a) 0.245...
Given a survivor of the titanic is a man, what is the probability rounded to the nearest whole percent the survivors was a second class passenger based on the data? (Table)
If X is the radius of the sphere that is a uniform continuous random variable on [3, 5] what is the expected value of the volume of the sphere?
The mean per capita income is $19,695 per annum with a variance of 802,816. What is the probability that the sample mean would differ from the true mean by less than $158 if a sample of 226 persons...
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