Use Normal Distributions

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Presentation transcript:

Use Normal Distributions Section 11.3

Objectives: Find normal probabilities Interpret normal distributions

Key Vocabulary: Normal distribution Normal curve Standard Normal Distribution z-score

Normal Distributions and Normal Curves A normal distribution is modeled by a bell-shaped curve called a normal curve that is symmetric about the mean

Areas Under a Normal Curve (Page 757)

Example 1: A normal distribution has mean and standard deviation σ. For a randomly selected x-value from the distribution, find .

Example 2: The blood cholesterol readings for a group of women are normally distribution with a mean of 172 mg/dl and a standard deviation of 14 mg/dl. About what percent of the women have reading between 158 and 186? Readings higher than 200 are considered undesirable. About what percent of the readings are undesirable?

#1: A normal distribution has mean and standard deviation #1: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

#2: A normal distribution has mean and standard deviation #2: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

#3: A normal distribution has mean and standard deviation #3: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

#4: A normal distribution has mean and standard deviation #4: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

#5: A normal distribution has mean and standard deviation #5: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

#6: A normal distribution has mean and standard deviation #6: A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution.

Standard Normal Distribution The standard normal distribution is the normal distribution with mean 0 and standard deviation 1. The formula below can be used to transform x-values into standard normal distribution. The z-value for a particular x-value is called the z-score and is the number of standard deviations the x-value lies above or below the mean.

Standard Normal Table Page 759

Example 3: Scientist conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each survey. The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of 14.1 seals. Find the probability that at most 50 seals were observed during a survey.

#8: Complete. In Example 3, find the probability that at most 90 seals were observed during a survey.

#9: Complete. Explain why it makes sense that .

Homework Assignment Page 760 #4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 32, 34