For a certain type of salamander, the mass X of a randomly chosen adult is normally distributed. . If 95% of adults in this species have a mass between 6.7 grams and 8.1 grams, what can we infer about the likely mean and standard deviation of X? Tell me about your process in coming up with a distribution. Sketch a graph of the distribution of X, with the mean and standard deviation shown. You can either sketch the graph and use it to determine the mean and standard deviation, or find it another way and then sketch it to illustrate.
For a certain type of salamander, the mass X of a randomly chosen adult is normally distributed. . If 95% of adults in this species have a mass between 6.7 grams and 8.1 grams, what can we infer about the likely mean and standard deviation of X? Tell me about your process in coming up with a distribution. Sketch a graph of the distribution of X, with the mean and standard deviation shown. You can either sketch the graph and use it to determine the mean and standard deviation, or find it another way and then sketch it to illustrate.
For a certain type of salamander, the mass X of a randomly chosen adult is normally distributed. . If 95% of adults in this species have a mass between 6.7 grams and 8.1 grams, what can we infer about the likely mean and standard deviation of X? Tell me about your process in coming up with a distribution. Sketch a graph of the distribution of X, with the mean and standard deviation shown. You can either sketch the graph and use it to determine the mean and standard deviation, or find it another way and then sketch it to illustrate.
I'm asking for help with the "Application to Biology-Normal Distributions" portion up to the bullet point that starts with "For each of the following probabilities..."
Transcribed Image Text:Application to Biology - Normal Distributions
For a certain type of salamander, the mass X of a randomly chosen adult is normally distributed.
• If 95% of adults in this species have a mass between 6.7 grams and 8.1 grams, what can we infer about
the likely mean and standard deviation of X? Tell me about your process in coming up with a
distribution. Sketch a graph of the distribution of X, with the mean and standard deviation shown. You
can either sketch the graph and use it to determine the mean and standard deviation, or find it another
way and then sketch it to illustrate.
For each of the following probabilities, sketch a graph of the distribution of X illustrating the
calculation. Then find the probability using technology, telling me how you choose the computation you
tell the technology to do for you.
P(X<7)
P (6.8 < X < 7.1)
P(X> 8.6)
. Find the z scores associated to the values above, and explain how they are related to the standard
deviation of X. Sketch the standard normal distribution and illustrate the associated probabilities. How
do they compare with your original illustrations?
Find the mass of a salamander with a z score of z = -1.2 and explain your reasoning. Illustrate on both
the standard normal distribution and the original distribution for X.
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Suppose you have a salamander which is in the 88th percentile for mass.
• What is its mass? Tell me about how you find this, and illustrate on the distribution of X.
. What is its z score? Tell me about how you find this, and illustrate on the standard normal
distribution.
• What is the probability that a randomly chosen salamander will have a greater mass? Tell me about
how you find this, and illustrate on both the standard normal distribution, and on the distribution of
X.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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