6.08 the normal distribution

standard deviation

a data measure that states how far, on average, every value is from the mean

Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a mean of 450 seconds and a standard deviation of 50 seconds. Suppose there are 160 emergencies in that town.In about how many emergencies are the response times expected between 400 seconds and 500 seconds?

109

The weights of bags of ready-to-eat salad are normally distributed with a mean of 300 grams and a standard deviation of 9 grams. What percent of the bags weigh less than 291 grams?

16%

The weight of a soccer ball is normally distributed with a mean of 0.43 kg and a standard deviation of 0.01 kg. Suppose 800 different soccer balls are in a warehouse. About how many soccer balls weigh more than 0.45 kg?

20 . The standard deviation of 0.01 kg. 0.45 is two standard deviation above. 50%+47.5% =97.7% are balls that are less than 0.45 kg. Hence, 20 soccer balls weigh more than 0.45 kg,

empirical rule

In normally distributed data, about 68% of the data is within one standard deviation of the mean, 95% of the data is within two standard deviations of the mean, and 99.7% of the data is within three standard deviations of the mean. The empirical rule states that data in a normal distribution have the following traits. Note that the Greek letter μ, pronounced "mu", represents the mean and σ (sigma) represents the standard deviation.

Select Yes or No to state whether each data set is likely to be normally distributed.

Normally distributed: the number of eggs collected each week on a large farm the weight of eggs in the kitchen of a resteraunt Not normally distributed: the number of yolks in randomly selected eggs the number of eggs in cartons sold at a supermarket

Suppose the heights of professional horse jockeys are normally distributed with a mean of 62 in. and a standard deviation of 2 in. Which group describes 16% of the population of horse jockeys?

jockeys who are taller than 64 in. jockeys who are shorter than 60 in.

Real-world data sets, if large enough in size, often follow a symmetrical distribution known as a normal distribution. A normal distribution is a probability distribution that is symmetrical around the mean . In other words, most of the data is normal or average, with fewer and fewer data points as you get farther above or farther below the mean. Also, the half above the mean and the half below the mean are mirror images of each other; each containing 50% of the data. The graph of a normal distribution resembles a bell. That is why it is often referred to as a bell-shaped graph.

normal distribution: bell-shaped distribution, centered on the mean mean: The average value of a data set

Normal distributions and related formulas use Greek letters.

μ (Greek letter mu) : denotes the mean of a population. σ (Greek letter lowercase sigma) : denotes the standard deviation of a population.