Question

need some assistance

both questions please

Question 4 (Two parts; 7 marks In total): Chronic back pain has become common in children due to carrying heavy backpacks to school. In a certain population of children, the volumes of backpacks they carry are normally distributed with a mean of 620 cubic inches and a standard deviation of 110 cubic inches. (a) Determine the percentage of these backpacks that have volumes between 580 and 850 cubic inches. (4 marks) I (b) Determine the 75 percentile of the volumes of these backpacks. (3 marks) Question 5 (3 marks): The distribution of the number of TVs per household in a certain city is strongly right skewed with a mean of 2.1 TVs and a standard deviation of 1.8 TVs. Describe the sampling distribution of the sample mean for random samples of 60 households, explaining the logic of your answer. w

Answer 1

Question 4:

(a) z = (x - µ)/σ = (580 - 620)/110 = -0.36

P (z = -0.36) = 0.3581

z = (x - µ)/σ = (850 - 620)/110 = 2.09

P (z = 2.09) = 0.9817

Required probability = 0.9817 - 0.3581 = 0.6237

(b) z = 0.67

x = 0.67*110 + 620 = 694.19

Question 5:

The sampling distribution is:

µ = 2.1

σ = σ/√n = 1.8/√60 = 0.23

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