The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 212.50 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 200.30 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? ..... a. The probability is 0.1151, (Round to four decimal places as needed.) b. The probability is . (Round to four decimal places as needed.)

Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in the following table. Reaction None Mild Strong Column Total Within 5 Minutes After 5 Minutes 391 65 44 500 66 341 93 500 Row Total 457 406 137 1000 Let's use the following notation for the various events: W= washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.)

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Thank you!! everything was pretty much right except for part (d) it did not take the 105

3(6+4)2-5(17-20)2

2000=(15)(c)(35)

82-2(8)(3)+32