A population has a mean μ = 70 and a standard deviation o=36. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 81. =(Simplify your answer.) = (Simplify your answer.)
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- ssume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the following: The Z-value that separates the bottom 18% from the others. The Z-Value for the 95 percentile. What is the IQ score that separates the bottom 18% from the others? The 95 percentile is? A. 113.725 B. -.92 C. 75.325 D. -.915 E. 1.645 F. 86.275 G. 124.675 H. .915The data in the table represent the ages of the winners of an award for the past five years. Use the data to answer questions (a) through (c). 25 30 61 48 42 a. Determine the population mean age, μ, of the five winners. μ=________________ (Type an integer or a decimal.) b. Consider samples of size 3 without replacement. Find the mean of the variable x. Ages x Ages x Full data set 25, 30, 61 38.67 25, 48, 42 38.33 25, 30, 48 34.33 30, 61, 48 46.33 25, 30, 42 32.33 30, 61, 42 44.33 25, 61, 48 44.67 30, 48, 42 40.00 25, 61, 42 42.67 61, 48, 42 50.33 The mean of the variable x is ______________. (Round to two decimal places as needed.) c. Find μx, using only the result of part (a). μx=_________________ (Type an integer or a decimal.)Example For 100 observations, the arithmetic mean and standard deviation are 8 and V10.5 · For 50 observations selected from these 100 observations, the mean and standard deviation are 10 and 2 respectively. Find the mean and standard deviation of the other half.
- Examples A population has a mean of 110 and a standard deviation of 6. A random sample of 20 measurements is drawn from this population. Describe the sampling distribution of the sample means by computing its mean and standard deviation. Steps Solution 1. Identify the given information. µ = 110, o = 6, and n=20 2. Find the mean of the sampling distribution. Use the property that ux_= µ. =110 3. Find the standard deviation of the sampling distribution. Use the property that "X = 1.3420 The grades of Senior High School learners in Statistics is normally distributed with mean of 84 and standard deviation of 2.75. If 45 samples consisting of 30 learners each are drawn from the population, what would be the expected mean and standard deviation of the resulting sampling distribution of the means? Steps Solution 1. Identify the given information. H = 84, o = 2.75, and n= 30 2. Find the mean of the sampling distribution. Use the property that ux_= µ. =84 3. Find the standard deviation of the…The frequency distribution was obtained using a class width of 0.5 for data on cigarette tax rates. Use the frequency distribution to approximate the population mean and population standard deviation. Compare these results to the actual mean u = $1.481 and standard deviation a = $0.971. E Click the icon to view the frequency distribution for the tax rates. The population mean is S. (Round to three decimal places as needed.) Frequency distribution cigarette tax rates - X The population standard deviation is S (Round to three decimal places as needed.) Tax Rate 0.00-0.49 0.50-0.99 1.00-1.49 1.50-1.99 2.00-2.49 2.50-2. 99 3.00-3.49 3.50-399 4.00 4.49 Frequency O Compare these results to the values found using the actual data. 14 O A. The grouped values are both slightly larger. O B. The grouped values are both slightly' smaller. O C. The grouped mean is slightly larger, while the grouped standard deviation is slightly smaller. 17 O D. The grouped mean is slightly smaller, while the…A distribution of values is normal with a mean of 190 and a standard deviation of 4.Find the interval containing the middle-most 30% of scores: Enter your answer using interval notation. Example: (2.1,5.6)
- Calculus The height of 700 boys are found to approximately follow such a distribution, with a mean height of 148 cm and a standard deviation of 19 cm. Find the number of boys with heights between 129 cm and 167 cm.Refer to the data set in the accompanying table. Assume that the paired sample data is a simple random sample and the differences have a distribution that is approximately normal. Use a significance level of 0.05 to test for a difference between the weights of discarded paper (in pounds) and weights of discarded plastic (in pounds). E Click the icon to view the data. In this example, Hg is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the weight of discarded paper minus the weight of discarded plastic for a household. What are the null and alternative hypotheses for the hypothesis test? O A. Ho: Ha = 0 H,: Ha #0 O B. Ho: Ha #0 H1: Hd =0 O C. Ho: Ha #0 O D. Ho: Ha = 0 H1: Hd 0The ages (in years) of a random sample of shoppers at a gaming store are shown. Determine the range, mean, variance, and standard deviation of the sample data set. 12, 19, 23, 14, 16, 16, 22, 16, 15, 19 The range is (Simplify your answer.) The mean is (Simplify your answer. Round to the nearest tenth as needed.) The variance is (Simplify your answer. Round to the nearest tenth as needed.) The standard deviation is (Simplify your answer. Round to the nearest tenth as needed.)
- Player His Average Points Other's Average Points Other's Standard Deviation Fredo 153 163 15 Karl 163 183 35 Table 2.57 a. Which player had the higher average points when compared to the other players on his team? Fredo O Karl b. Use Table 2.57 to find the value that is three standard deviations above the mean for each team. Enter the exact answers. Fredo's team: Number Karl's team: Number C. Use Table 2.57 to find the value that is three standard deviations below the mean for each team. Enter the exact answers. Fredo's team: Number Karl's team: Number Next Back Question Menu- Quit & Save Submit Assignment 502 PM 200A distribution of values is normal with a mean of 120 and a standard deviation of 4.Find the interval containing the middle-most 68% of scores: Enter your answer using interval notation. Example: (2.1,5.6)The numbers of courses taught per semester by a random sample of university professors are shown in the histogram. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the data set. 25- 24 20- 17 16 15 10- 5- Number of courses taught per semester f 1 2 16 24 4 17 The sample mean is x = 2.9 (Round to one decimal place as needed.) The sample standard deviation is s = (Round to one decimal place as needed.) Number of professors