Question

Question 7 5 pts According to research, the amount of sleep per night for U.S adults follows a normal distribution with a mean p = 7.25 hours and standard deviation o - 1.25 hours. Determine the proportion of people who get between 5.0 and 9.0 hours of sleep per night. Use the provided Standard Normal Table (Z table), and provide the proportion as a decimal rounded to four decimal places.

Answer 1

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Step 1: Sketch the curve. The probability that 5<x<9 is equal to the blue area under the curve. 0.40 0.35 0.30- 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 3 00 4 5 6 7 8 9 10 11 12 Step 2: Since = 7.25 and o= 1.25 We have: P(5<x< 9 ) = P(5 – 7.25 < X – 4 < 9 – 7.25 ) = P ( 57,25 < > ( 5 – 7.25 X - u <- 9 – 7.25 1.25 Since z = 2, 573 = -1.8 and 97% = 1.4 We have: P(5< X < 9) = P( - 1.8 < 3 < 1.4) Step 3: Use the standard normal table to conclude that: P( - 1.8<<<1.4) = 0.8833