Question

People in hot-air balloons usually fly just above the treetops at between 250 and 500 feet. In populated areas, however, they usually stay at an altitude of at least 1000 feet. The amount of flying time possible in a hot-air balloon is dependent on many factors: number of propane burners, number of people in the balloon, and weather. Assume the time spent aloft is normally distributed with a mean of 1.5 hours and a standard deviation of 0.45 hours. Approximately 33% of all hot-air balloon flights last more than _____ hours? (5 points) 5. A national survey found that Americans drink an average of 6 glasses of water per day. The Association of Medical Doctors recommends 8 glasses per day be consumed by adults. Assume the number of glasses of water consumed per day is normally distributed with a mean of 6 glasses and a population standard deviation of 1.7 glasses. An adult is selected at random, and is asked how many of water did you drink yesterday? What is the probability that the response is more than 6 glasses but less than 8 glasses? (5 points)

Answer 1

4)

z value at 33% = 0.95
mean = 1.5 , s = 0.45

z = (x - mean)/sigma
0.95= ( x - 1.5)/0.45
x = 0.45*0.95 + 1.5
x = 1.93

5)

Here, μ = 6, σ = 1.7, x1 = 6 and x2 = 8. We need to compute P(6<= X <= 8). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (6 - 6)/1.7 = 0
z2 = (8 - 6)/1.7 = 1.18

Therefore, we get
P(6 <= X <= 8) = P((8 - 6)/1.7) <= z <= (8 - 6)/1.7)
= P(0 <= z <= 1.18) = P(z <= 1.18) - P(z <= 0)
= 0.881 - 0.5
= 0.381