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Name: ________________________Normal DistributionDescribe what it means for something to be normally distributed.What is an experiment or situation you could create using 3-5 dice that will be normally distributed? Describe it below and include the necessary materials/dice. Be sure to explain why you think your situation will be normally distributed.Create a frequency table for you situation and run 30 trials below:Graph your data:Is your data normally distributed? How do you know?Find someone else who did the same experiment and create a graph for the combined data.How is your graph similar or different when you use the combined data?What is the empirical rule for normally distributed data and why is it useful?The mean height of players in a basketball competition is 184 cm. If the standard deviation is 5 cm, without a calculator find the percentage of players that are likely to be:– Taller than 189 cm– Taller than 179 cm– Between 174 cm and 199 cm– Over 199 cmOne shorthand method to communicate information about normally distributed data more efficiently is to write it in the form X ~ N (?, σ2). Rewrite the information about basketball players in this form.Based upon what you know about binompdf and binomcdf, how could you use normalpdf and normalcdf to help determine probabilities?Use the calculators to determine the following probabilities, given X~N(10, 2.32). include with each problem a shaded illustration of the situation:a. P (8 ≤ X ≤ 11)b. P (X ≤ 12)c. P (X > 9)c. P (10.4 ≤ X ≤ 14)What is a z-score and why is it useful to us?Create a general equation that will allow you to change any normal X-distribution into a standard normal distribution, also known as a Z-distribution.The table alongside shows Sergio’s results in his final examinations, along with the class means and standard deviations. Sergio?σPhysics73%78%10.8%Chemistry77%72%11.6%Mathematics76%74%10.1%German91%86%9.6%Biology58%62%5.2% Find Sergio’s Z-value for each subjectArrange Sergio’s performances in each subject from best to worst.The inverse normal function will also be an immensely helpful tool to us. How is it different than what we have been doing so far?The number k is known as a quantile. Find the 95% quantile for the basketball players from before.Suppose Z is the standard normal distribution. Illustrate with a sketch then find k such that P (Z ≤ 0.58)Given that X~N(23, 52), find a such that P (23 – a < X < 23 + a) = 0.427.The lengths of metal rods produced in a manufacturing process are normally distributed with a mean ? cm and standard deviatio 6 cm. 5.63% of the rods have length greater than 89.52 cm. Find the mean, median, and modal length of the metal rods.A student arrives at a school X minutes after 08:00, where X may be assumed to be normally distributed. On a particular day it is observed that 40 % of the students arrive before 08:30 and 90 % arrive before 08:55.(a)Find the mean and standard deviation of X.(b)The school has 1200 students and classes start at 09:00. Estimate the number of students who will be late on that day. (c)Maelis had not arrived by 08:30. Find the probability that she arrived late.After being sprayed with a weedkiller, the survival time of weeds in a field is normally distributed with a mean of 15 days.(a)If the probability of survival after 21 days is 0.2, find the standard deviation of the survival time. When another field is sprayed, the survival time of weeds is normally distributed with a mean of 18 days.(b)If the standard deviation of the survival time is unchanged, find the probability of survival after 21 days.The speeds of cars at a certain point on a straight road are normally distributed with mean ? and standard deviation σ. 15 % of the cars travelled at speeds greater than 90 km h–1 and 12 % of them at speeds less than 40 km h–1. Find ? and σ.The weight loss, in kilograms, of people using the slimming regime SLIM3M for a period of three months is modelled by a random variable X. Experimental data showed that 67 % of the individuals using SLIM3M lost up to five kilograms and 12.4 % lost at least seven kilograms. Assuming that X follows a normal distribution, find the expected weight loss of a person who follows the SLIM3M regime for three months. ................
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