Question

1) Find the following probabilities: a) Pr{Z < 0.67} b) Pr{Z ≥ -0.67} c) Pr{-2.05 < Z < 2.05} d) Pr{-2.91 < Z < 0.31} e) Pr{Z < -2.03 or Z > 2.03} (you want the probability that Z is outside the range -3.03 to 3.03)

2) Assuming that for the height of women, μ = 65.2 inches and σ = 2.9 inches, find the following: a) Pr{Y > 65.7} b) Pr{Y < 57.8} c) Pr{60 < Y < 69}

3) Refer to problem (2). Give the following percentiles: a) 98 b) 78 c) 22

4) Blood calcium levels are measured in mg/dL. In patients over 30, μ = 9.7 mg/dL, and σ = 2.42 mg/dL. a) Give the blood calcium values for the middle 60% of patients. b) Give the blood calcium values for the middle 80% of patients. c) Give the 90th percentile. d) Are you surprised by the answers to (b) and (c)? Explain. If you're not sure what's going on, draw some pictures of the normal curves.

Answer 1

Solution:-

4)

μ = 9.7 mg/dL, and σ = 2.42 mg/dL

a) The blood calcium values for the middle 60% of patients is 7.66 and 11.74.

p-value for the middle 60% = 0.20 and 0.80

z-score for the p-value = + 0.842

By applying normal distruibution:-

x₁ = 7.66

x₂ = 11.737

b) The blood calcium values for the middle 80% of patients is 6.598 and 12.802.

p-value for the middle 80% = 0.10 and 0.90

z-score for the p-value = + 1.282

By applying normal distruibution:-

x₁ = 6.598

x₂ = 12.802

c) 90th percentile is 12.802

p-value for the bottom 90% = 0.90

z-score for the p-value = 1.282

By applying normal distruibution:-

x = 12.802

d) The upper limit of the middle 80% of the distribution is equal to the 90th percentile of the distribution.