Question

1) Determine the following areas under the standard normal (z) curve.

a) Between -1.5 and 2.5

2) Consider babies born in the "normal" range of 37–43 weeks gestational age. A paper suggests that a normal distribution with mean μ = 3500 grams and standard deviation σ = 599 grams is a reasonable model for the probability distribution of the continuous numerical variable x = birth weight of a randomly selected full-term baby.

a) How would you characterize the most extreme 0.1% of all full-term baby birth weights? (Round your answers to the nearest whole number.) The most extreme 0.1% of birth weights consist of those greater than ____ grams and those less than ____ grams.

b) If x is a random variable with a normal distribution and a is a numerical constant (a ≠ 0), then y = ax also has a normal distribution. Use this formula to determine the distribution of full-term baby birth weight expressed in pounds (shape, mean, and standard deviation), and then recalculate the probability from part (d). (Round your answer to four decimal places.)

3) The two intervals (114.7, 115.9) and (114.4, 116.2) are confidence intervals (computed using the same sample data) for μ = true average resonance frequency (in hertz) for all tennis rackets of a certain type.

a) What is the value of the sample mean resonance frequency? (Hint: Where is the confidence interval centered?) ______ Hz

Answer 1