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Sampling Distribution and the Central Limit, Exams of Mathematics

The University of Mississippi (Ole Miss)Mathematics

A series of questions and answers related to sampling distribution and the central limit theorem. It covers topics such as the use of normal distribution to approximate sampling distribution, mean and standard deviation of sampling distribution, and the difference between individuals and groups in sampling distribution. likely to be useful as study notes or exam preparation for a statistics course at the university level.

Typology: Exams

2022/2023

Available from 10/23/2023

WhitneyDarren
WhitneyDarren 🇺🇸

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SAMPLING DISTRIBUTION AND THE CENTRAL LIMIT
MATH 115- Introduction to Statistics, 2023
University of Mississippi
1. A sampling distribution refers to groups rather than individuals. Is it True or False
Answer: False.
2. Decide if the statement is True or False: A simple random sample of size 16 is
obtained from a population that is skewed left with a mean of 59 and a standard
deviation of 7. A normal distribution can be used to approximate the sampling
distribution of sample means.
Answer: True.
3. A study on the latest fad diet claimed that the amounts of weight lost by all people on
this diet had a mean of 24.3 pounds and a standard deviation of 7.7 pounds. Step 1 of
2: If a sampling distribution is created using samples of the amounts of weight lost by
54 people on this diet, what would be the mean of the sampling distribution of sample
means? Round to two decimal places, if necessary.
Answer: The mean of the sampling distribution of sample means is 1.05 pounds
4. Find the mean of the sampling distribution of sample means using the given
information. Round to one decimal place, if necessary. μ=49 and σ=9; n=16
Answer: The mean of the sampling distribution of sample means is 49.
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SAMPLING DISTRIBUTION AND THE CENTRAL LIMIT

MATH 115- Introduction to Statistics, 2023

University of Mississippi

  1. A sampling distribution refers to groups rather than individuals. Is it True or False Answer: False.
  2. Decide if the statement is True or False: A simple random sample of size 16 is obtained from a population that is skewed left with a mean of 59 and a standard deviation of 7. A normal distribution can be used to approximate the sampling distribution of sample means. Answer: True.
  3. A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 24.3 pounds and a standard deviation of 7.7 pounds. Step 1 of 2: If a sampling distribution is created using samples of the amounts of weight lost by 54 people on this diet, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary. Answer: The mean of the sampling distribution of sample means is 1.05 pounds
  4. Find the mean of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=49 and σ=9; n= Answer: The mean of the sampling distribution of sample means is 49.
  1. Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9 years with a standard deviation of 1.0 years. Step 2 of 2: If a sampling distribution is created using samples of the ages at which 70 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary. Answer: Rounded to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.12 years.
  2. A simple random sample of size 24 is obtained from a population that is normally distributed with a mean of 44 and a standard deviation of 4. A normal distribution can be used to approximate the sampling distribution of sample means. Is it True or False? Answer: True
  3. Suppose a random sample of 25 measurements is selected from a population with mean 58 and standard deviation 10. Step 1 of 2: Find the mean of the sampling distribution of sample means using the given information. Round to two decimal places, if necessary. Answer: The standard deviation of the sampling distribution of sample means is 2.
  4. Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=52 and σ=9; n= Answer: Rounded to one decimal place, the standard deviation of the sampling distribution of sample means is approximately 1.3.
  5. Decide if the statement is True or False. A sampling distribution refers to groups rather than individuals. Answer: True

53 people on this diet, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary. Answer: Rounded to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 1.07 pounds

  1. Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ=50 and σ=9; n= Answer: The standard deviation of the sampling distribution of sample means is 1.8.
  2. Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.5 years with a standard deviation of 1.2 years. Step 2 of 2: If a sampling distribution is created using samples of the ages at which 48 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary Answer: The standard deviation of the sampling distribution of sample means is approximately 0.17 years.
  3. Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 61people is taken. Step 2 of 2 : What is the probability that the mean IQ score of people in the sample is less than 96? Round your answer to 4 decimal places, if necessary. Answer: The probability that the mean IQ score of people in the sample is less than 96 is approximately 0.
  1. Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.8 feet and a standard deviation of 0.4 feet. A sample of 75 men’s step lengths is taken. Step 2 of 2: Find the probability that the mean of the sample taken is less than 2.4 feet. Round your answer to 4 decimal places, if necessary. Answer: The probability that an individual man's step length is less than 2.4 feet is approximately 0.
  2. Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 126 millimeters, and a variance of 64. If a random sample of 39 steel bolts is selected, what is the probability that the sample mean would be greater than 122.6 millimeters? Round your answer to four decimal places. Answer: The probability that the sample mean of 39 steel bolts is greater than 122.6 millimeters is approximately 0.