z score= (obseration-mean)/standard deviation. z score means how many times stabdard deviations a data point away from the mean.
hence a. z score=(65-57)/11=8/11=0.72
b. z score= (21-57)/11=-36/11=-3.27
c. the obseravtion 21 is an outlier.
why? because a z score(abosolute value) of 3 or above means the probability of getting that value is less than 0.3%. 99.7% of the data is within the -3<z<3 range. hence we can say that the score 21 is an outlier.
or we can say that a 99.7% of the data is within 3 standard deviation of the mean. that means 99.7% of the data is within 57-11x3=24 and 57+33=90. hence 21 is an outlier.
in the graph we can see that probability of getting a value less than 24 is very less (represented by the red area) hence finding 21 is rarer than this hence 21 is an outlier.
4. reasons we find outliers;
1. if we record the data wrong.
2. if the observation is characteristically different from the other observations
3.inconsistent sampling.
4. the environment in which the observation is made is different from other observations.
7. A sample dataset has a mound-shaped and symmetric distribution with mean of 57 and a...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 15 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 14.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left. No, the x distribution...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 9 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 8.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. No, the x distribution is skewed left. No, the...
1. A distribution of measurements is relatively mound-shaped with a mean of 60 and a standard deviation of 11. Use this information to find the proportion of measurements in the given interval. between 49 and 71 2. A distribution of measurements is relatively mound-shaped with a mean of 80 and a standard deviation of 12. Use this information to find the proportion of measurements in the given interval. greater than 92 3. A distribution of measurements has a mean of...
(20) 12. Suppose that the mean of a sample of mound-shaped data is 40 and the standard deviation is 4. (4) a. What would the x value of the sample be if it was 1.5 standard deviations above the mean? (4) b. What is the z value if the data point was 50? (2) c. Using the Empirical rule, what is the probabilty that the data is between 36 and 48? Explain how you made this calculation (2) d. Using...
A distribution of measurements is relatively mound-shaped with a mean of 80 and a standard deviation of 14. Use this information to find the proportion of measurements in the given interval. Greater than 94
12. Suppose that the mean of a sample of mound-shaped data is 40 and the standard deviation is 4. (4) a. Use the Empirical rule to state the probability that the data is one, two, and three standard deviations from the mean and state the intervals for each of these. (4) b. Use the Tchebysheff’s theorem to state the probability that the data is 1, 1.5, 2, and 3 standard deviations from the mean and state the intervals for each...
A random sample of size 10 selected from a bell-shaped distribution has a mean equal to 11 and a standard deviation equal to 5.4. For this sample, what is the Z-score for a measurement of 22? AO +11 BO 2.04 CO -11 D O -2.04 E O 1.1 Submit Answer
Consider a distribution with a mean of 15 and a standard deviation of 3. If an observation from the distribution has a z-score of -2, what is the value? Consider a distribution with a mean of 15 and a standard deviation of 3. If an observation from the distribution has a z-score of -2, what is the value?
Question 4 (10 points): A distribution of measurements is relatively mound-shaped with mean 45 and standard deviation 15 (a) What proportion of the measurements will fall between 30 and 60? (b) What proportion of the measurements will fall between 15 and 75? (c What proportion of the measurements w fall between 30 and 75? (d) If a measurement is chosen at random from this distribution, what is the probability that it will be greater than 60?
Problem 1 (18 points) Suppose the distribution of fuel efficiency (miles per gallon (mpg) in highway driving) for a sample of cars has a mound-shaped and symmetric distribution with mean x =38 and standard deviation s = 10 points. Illustrate your answers with graphs. a. Calculate the percent of cars whose fuel efficiency is less than 48 mpg. b. Calculate the percent of scores that are between 28 and 68 mpg. c. Calculate the 16th percentile of the data.