CALCULATING STANDARD DEVIATION WORKSHEET



Name: October 13th 2015Stats 1Stats.18.z-scores – Notes and PracticeZ-Scoresright635000For All Normal Distributions______ of the data is above, and ______ is below the mean of the data.Approximately ______ of the data occurs within ___ Standard Deviation of the meanApproximately ______ of the data occurs within ___ Standard Deviation of the meanApproximately ______ of the data occurs within ___ Standard Deviation of the meanExample AIf the diameter of a basketball is normally distributed, with a mean?(μ)?of 9″, and a standard deviation?(σ)?of 0.5″, what is the probability that a randomly chosen basketball will have a diameter between 9.5″ and 10.5″?48867701300Example BIf the height of women in the U.S. is normally distributed with μ=5′8′′ and σ=1.5′′, what is the probability that a randomly chosen woman in the U.S. is shorter than 5′5″?161511624000Quick PracticeA normally distributed data set has μ=10 and σ=2.5, what is the probability of randomly selecting a value greater than 17.5 from the set?center762000A normally distributed data set has μ=.05?and σ=.01, what is the probability of randomly choosing a value between .05 and .07 from the set?center63500A normally distributed data set has μ=514 and an unknown standard deviation, what is the probability that a randomly selected value will be less than 514?center295400If we want to know the _______________ of the population _________, _________, or ____________ any values … we can use the z-score!The Z-Score tells us the number of _____________ _________________ between any ____________ and the __________ of the population.center571500center698500Example CWhat is the?z-score of a value of 27, given a set mean of 24, and a standard deviation of 2?Example DWhat is the z-score of a value of 104.5, in a set with μ=125 and σ=6.2?Quick Practice51509533423What is the probability of a z-score… less than 0.54??greater than 0.54?less than -0.93??greater than -0.93??greater than 0.81??less than -0.81?0What is the probability of a z-score… less than 0.54??greater than 0.54?less than -0.93??greater than -0.93??greater than 0.81??less than -0.81?What is the?z-score of the price of a pair of skis that cost $247, if the mean ski price is $279, with a standard deviation of $16?What is the?z-score of a 5-scoop ice cream cone if the mean number of scoops is 3, with a standard deviation of 1 scoop?What is the?z-score of the weight of a cow that tips the scales at 825 lbs, if the mean weight for cows of her type is 1150 lbs, with a standard deviation of 77 lbs?Examples – Using Z-Score TablesE. What is the probability that a value with a z-score less than 2.47 will occur in a normal distribution?F. What is the probability that a value with a z-score greater than 1.53 will occur in a normal distribution?G. What is the probability of a random selection being less than 3.65, given a normal distribution with μ=5?and?σ=2.2? ................
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