Homework Chapter 7 and 8 10. High school girls average 100 text messages daily. Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken. a. What is the probability that the sample mean is more than 105? 𝑝(𝑥 > 105) = 1 − 𝑝 (𝑧 < 105 − 100 ) 20 √50 𝑝(𝑥 > 105) = 1 − 𝑝(𝑧 < 1.768) 𝑝(𝑥 > 105) = 1 − 0.9615 𝒑(𝒙 > 𝟏𝟎𝟓) = 𝟎. 𝟎𝟑𝟖𝟓 b. What is the probability that the sample mean is less than 95? 𝑝(𝑥 < 95) = 𝑝 (𝑧 < 95 − 100 ) 20 √50 𝑝(𝑥 < 95) = 𝑝(𝑧 < −1.768) 𝒑(𝒙 < 𝟗𝟓) = 𝟎. 𝟎𝟑𝟖𝟓 c. What is the probability the sample mean is in between 95 and 105? 𝑝(95 < 𝑥 < 105) = 𝑝 (𝑧 < 105 − 100 95 − 100 ) − 𝑝 (𝑧 < ) 20 20 √50 √50 𝑝(95 < 𝑥 < 105) = 𝑝(𝑧 < 1.768) − 𝑝(𝑧 < −1.768) 𝑝(95 < 𝑥 < 105) = 0.9615 − 0.0385 𝒑(𝟗𝟓 < 𝒙 < 𝟏𝟎𝟓) = 𝟎. 𝟗𝟐𝟐𝟗 24. The popularity of then President Sarkozy had an approval rating of 26%. a. P(fewer than 60 of 200 French people gave him a favorable rating? 𝑝(𝑥 < 0.3) = 𝑝 𝑧 < ( 𝑝(𝑥 < 0.3) = 𝑝 𝑧 < ( 𝑝̂ − 𝑝 √𝑝(1 − 𝑝) ) 𝑛 0.3 − 0.26 √0.26(1 − 0.26) ) 200 𝑝(𝑥 < 0.3) = 𝑝(𝑧 < 1.2897) 𝒑(𝒙 < 𝟎. 𝟑) = 𝟎. 𝟗𝟎𝟏𝟒 b. P(More than 150 of 200 gave unfavorable rating)? 𝑝(𝑥 < 0.25) = 𝑝 𝑧 < ( 𝑝(𝑥 ...
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