Use the Central Limit Theorem to find p^ and σp^ Ĭalculate the z-score for p^ and move the slider along the x-axis to the appropriate z-score Only select between less than, greater than, and area between graphs.) (Note - there are four graphs available to choose from. Use the graph below to determine the probability that in a sample of 45 games, 30 or fewer of them were completed in less than 49 minutes.ĭrag and move the blue dot to select the appropriate probability graph area from the four options on the left. Of the 500 players that have completed the game, 331 of them completed the full game in less than 49 minutes. Before playing, the college student looked up statistics on how fast gamers we completing the full playthrough of the game. A college student recently purchased a multiplayer video game. Rounding to the nearest hundredth, we have P(p^>50)=0.84. Slide the black dots to the z-score we found above: −1. The Central Limit Theorem for sample proportions tell us that p^ is normally distributed with mean μp^=p and σp^=p(1−p)n−−−−−√. In order to calculate the z-score, so we need to identify μp^, and calculate p^ and σp^. This is greater than 10, so we may proceed and use the standard curve graph above to find our probability.Ģ. Next, we will check that the Central Limit Theorem for Sample Proportions applies. We are given a population proportion of p=0.57. since |−0.65|0.50), the probability that the sample proportion p^ will be more than 50%=0.50. Fredo's average points per game is 0.65 standard deviations less than his team mean.īut, since Fredo's z-score is −0.65, the distance from this to the mean is less than 0.9. Karl's average points per game is 0.9 standard deviations greater than his team mean. The z-score is the number of standard deviations a data value is from the mean of the data set. Karl's average points per game is 0.9 standard deviations greater than his teammates' average points per game.įredo's average points per game is closer to the team's mean than Karl's. Which of the following statements are true about how Karl and Fredo compare to their team in points per game? Select all that apply. The mean amount of points per game and standard deviations for their team were calculated. Karl and Fredo are basketball players who want to find out how they compare to their team in points per game. In which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?įind the z-score corresponding to each state. The mean price for the same sized home in Ohio is $170,000 with a standard deviation of $12,000. Take the square root, rounding to the nearest hundred.Ħ15,032,637−−−−−−−−−√=24,800 Based on the z scores found above, in which city would a home priced at 200,000 be closer to the mean price, compared to the distribution of prices in the city? In a recent national survey, the mean price for a 2000 sq ft home in Florida is $240,000 with a standard deviation of $16,000. The standard deviation is the square root of the sample variance of the living area of the five commercial buildings. The following data set provides information about the City of Somerville Assessors Valuation for the fiscal year 2016.įor commercial buildings, what is the sample standard deviation of the living area? Round your answer to the nearest hundred. Residential Total Assessed Land Value's standard deviation is 97,477. Residential Total Assessed Land Value's standard deviation is the smallest for those four, due to the narrowest range of data. Which has the smallest standard deviation? Residential Total Assessed Land Value The following data set provides infomation about the City of Somerville Assessors Valuation for the fiscal year 2016.įind the standard deviations for the commercial buildings total assessed land value and total assessed parcel value, and the residential buildings total assessed land value and total assessed parcel value.
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