Find the variance and standard deviation. Show your solution. 1. 1 2 3 4 P(x) 0.09 0.19 0.39 0.22 0.11
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A: E(X)=∑X.P(X)E(X)=0×0.11+1×0.22+2×0.33+3×0.44+4×0.55E(X)=0+0.22+0.66+1.32+2.2E(X)=4.4
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- Q.4. Use a test to discover whether given data are exponentially distributed or not. 0.09 0.29 0.35 0.38 0.52 0.63 1.33 1.41Examples 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…Medical School Applications A medical college dean read that the average number of applications a potential medical school student sends is 7.7. She thinks that the mean is lower than 7.7. So she selects a random sample of 28 applicants and asks each how many medical schools they applied to. The mean of the sample is 6.8. The population standard deviation is 2.5 . Test her claim at α=0.10. Assume that the variable is normally distributed. Use the P -value method with tables. State the hypotheses and identify the claim. :H0 ▼(Choose one) :H1 ▼(Choose one) This hypothesis test is a ▼(Choose one) test. Compute the test value. Always round z score values to at least two decimal places. z= Find the P-value. Round the answer to at least four decimal places. P-value= Make the decision. ▼(Choose one) the null hypothesis. Summarize the results. There is ▼(Choose one) that the average number of applications a potential medical school…
- Statistical PhysicsSite_A Site_B $115 $110$79 $79$40 $37$138 $129$96 $96$28 $28$84 $69$98 $98$116 $106$69 $66 Using software or a calculator, construct a 90% confidence interval comparing the population mean prices of all textbooks used that term at her college (price at Site A minus price at Site B). Interpret. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to three decimal places as needed.) A. It is plausible that the population mean price difference is 0 because 0 does not lie in the confidence interval left parenthesis nothing comma nothing right parenthesis .,. B. It is plausible that the population mean price difference is 0 because 0 lies in the confidence interval left parenthesis nothing comma nothing right parenthesis .,. C. It is not plausible that the population mean price difference is 0 because 0 does not lie…V. Find the variance and standard deviation. Show your solution. 1 0.19 2 0.39 4 0.11 P(x) 0.09 0.22 P(x) 0.11 0.22 0.33 0.44 0.55
- Heights of Models In a New York modeling agency, a researcher wishes to see if the average height of female models is really less than 67 inches, as the chief claims. A sample of 20 models has an average height of 65.8 inches. The standard deviation of the sample is 1.7 inches. At alpha = 0.05, is the average height of the models really less than 67 inches? Use the P-value method. Pleas show how to solve using the formulas, thanks!++ C. 0 52 a. The mean is b. The standard deviation is 2 58 Use the Empirical Rule to answer the following questions. Dn Test Scores 70 76 % of the test scores are between 58 and 70. % of the test scores are between 52 and 76. % of the test scores are between 46 and 82. % of the test scores are between 64 and 70. % of the test scores are less than 64. % of the test scores are less than 70. 82 Q4 n ex You used SS = x (x-x)² when calculating variance and standard deviation. An alternative formula for the standard deviation that is sometimes convenient for hand calculations is shown below. You can find the sample variance by dividing the sum of squares by n-1, and the sample standard deviation by finding the square root of the sample variance. Complete parts (a) and (b) below. (Ex)² SS = Ex². Click the icon for a table of the ages (in years) of shoppers at a local store. Data table 19 16 15 18 20 17 19 16 Shoppers' Ages 20 20 18 18 20 19 24 20 18 18 16 16 n X ar all Check answer