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Normal Probability problems

Author:
October 1st, 2022

Dear OTA,

Please help me in solving the following problems.
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Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees and a standard deviation of 1.00 degree C. A thermometer is randomly selected and tested. In each case, draw a sketch and find the probability of each reading.
a. Between 1.05 and 2.05

Question 2
Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ greater than 131.5.

Question 3
Assume that women’s heights are normally distributed with a mean given by u=63.6 in and a standard deviation given by o=2.5 in.
a. If 2 woman is randomly selected, find the probability that her height is greater than 63 inches.
b. If 100 women are randomly selected, find the probability that her height is between 63.5 inches and 64.5 inches.
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Thanks

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