Scores on a particular test, taken by a large group of students, follow a normal distribution with a variance of2500. A random sample of 25 scores was taken to estimate the population's mean score. Let the randomvariable x denote the sample mean. What is the probability that the interval (x - 30) to (x + 30) contains the truepopulation mean?Click the icon to view the standard normal table of the cumulative distribution function.The probability that the interval (x- 30) to (x+ 30) contains the true population mean is(Type an integer or decimal rounded to four decimal places as needed.)

Answered: Image /qna-images/answer/b7beb400-ca3d-4f36-b746-ff532cb1ec43.jpg

Answered: Scores on a particular test, taken by a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A random sample of 100 selected from a population with a standard deviation of 10 yielded a mean = 225. The mean and the standard deviation of the distribution of the sample means are ____________. 225 and 10 225 and 1 225 and 0.1 22.5 and 1 22.5 and 10
A study conducted by Hershey's discovered that Americans consumed an average of 11.4 pounds of chocolate per year. Let's assume that the annual chocolate consumption follows the Normal distribution with mean 11.4 pounds and a standard deviation of 3.6 pounds. Answer the following questions, performing all computations with Excel functions.
A random sample of a population of size n = 36, find the prob that the mean is between 110 and 115. The pop u is 100, and the sd is 15.
The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 20. What is the probability we could select a sample of 80 adults and find the mean of this sample is less than 95? 0.0125 0.9750 0.4875 0.9476
Among freshmen at a certain university, scores on the Math SAT followed the normal curve, with an average of 550 and an SD of 100. The SAT score of a student whose score is at the 75th percentile is closest to what value? 665 590 690 620
The Body Mass Index (BMI) of 60-year-old men follow a distribution that is approximately Normally distributed with a mean of 30 and a standard deviation of 6. Define the variable X, and state its distribution using the notation
For the population of one town, the number of siblings, x, is a random variable whose relative frequency histogram has a reverse J-shape. The mean number of siblings is 1.3 and the standard deviation is 1.5. Let x denote the mean number of siblings for a random sample of size 32. Determine whether the distribution of x is normal or approximately normal and find its mean and standard deviation.
What is the z-score of x = 3 if it is 2 standard deviation to the left of the mean? -3 -2 1 O 2 1.
Temperature in degrees Fahrenheit has been collected from a sample of 50 individuals. The mean is 98.5 and standard deviation is 3.2. If we convert each observation into degrees in the centigrade scale ((X°C × 9/5) + 32 = Y°F) then what would be the new mean and standard deviation of the set of temperatures?
Use the normal distribution of IQ scores , which has a mean of 90 and a standard deviation of 14, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity. view the table: Standard Scores and Percentiles for a Normal Distribution (cumulative values from the left) Full data set Open in StatCrunch + Copy to Clipboard + Open in Excel + Standard score % Standard score % minus−3.0 0.13 0.1 53.98 minus−2.5 0.62 0.5 69.15 minus−2 2.28 0.9 81.59 minus−1.5 6.68 1 84.13 minus−1 15.87 1.5 93.32 minus−0.9 18.41 2 97.72 minus−0.5 30.85 2.5 99.38 minus−0.1 46.02 3 99.87 0 50.00 3.5 99.98 The percentage of scores between 62 and 118 is ________%. Round to two decimal places as needed.
A random sample of 10,000 bottles of cola was taken to see whether the mean weight was 16 fluid ounces, as marked on the container. The null hypothesis is that the population mean is 16 ounces. Use the read-out below to test the hypothesis that the colas do not have a population mean of 16 fluid ounces. You do not have to do any calculations; just interpret the given data clearly and thoroughly in the context of the problem. | One-Sample T: ounces Test of u = 16 vs = 16 Variable Mean StDev SE Mean 95 CI T P ounces 10000 15.9988 0.0985 0.0010 (15.9969, 16.0007) -1.21 0.225
A normally distributed random variable has a mean of 449. If a score of 433 lies two standard deviations below the mean, find the variance of X.

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