Problem 1: [9 points] Weights X of female cats of a certain breed are normally distributed with mean μ = 4.1 kg and a standard deviation of σ = 0.6 kg. (a) What proportion of female cats have weights between 3.7 and 4.4 kg? [1] (b) A certain female cat has a weight that is 0.5 standard deviations (0.5σ) above the mean. What proportion of female cats are heavier than this one? [1] (c) Find the 80th percentile of the female cats' weights and interpret it. [3] (d) What is the likelihood that a randomly chosen female cat weighs more than 4.5 kg? [1] (e) Six female cats are chosen at random. Their weights are independent from one another. Let Y be the number out of those 6 whose weight is more than 4.5 kg. (i) What is the distribution of X? Give its expression. [2] (ii) Find the probability that exactly two have a weight more than 4.5 kg. [1]
Added by Ryan J.
Step 1
7 and 4.4 kg. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Sri K and 70 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Problem 1: [9 points] Weights X of female cats of a certain breed are normally distributed with mean μ = 4.1 kg and a standard deviation of σ = 0.6 kg. (a) What proportion of female cats have weights between 3.7 and 4.4 kg? [1] (b) A certain female cat has a weight that is 0.5 standard deviation (0.5σ) above the mean. What proportion of female cats are heavier than this one? [1] (c) Find the 80th percentile of the female cats weights and interpret it. [3] (d) What is the likelihood that a randomly chosen female cat weights more than 4.5 kg? [1] (e) Six female cats are chosen at random. Their weights are independent from one another. Let Y be the number out of those 6 whose weight is more than 4.5 kg. (i) What is the distribution of X? Give its expression. [2] (ii) Find the probability that exactly two have a weight more than 4.5 kg. [1]
Jason G.
Lucas F.
QUESTION 16 Assume that women's weights are normally distributed with a mean of 143 pounds and standard deviation 29 pounds. If a woman is randomly selected, find the probability that her weight is less than 140 pounds. Express your answer as a decimal using 4 decimal places. Give the exact value from the chart. Do not round your answer. QUESTION 17 Assume that women's weights are normally distributed with a mean of 143 pounds and standard deviation 29 pounds. If 100 women are randomly selected, use the central limit theorem to find the probability they have a mean weight less than 140 pounds. Express your answer as a decimal using 4 decimal places. Give the exact value from the chart. Do not round your answer. QUESTION 18 Assume that women's heights are normally distributed with a mean of 63.6 inches and standard deviation 2.5 inches. If one woman is randomly selected, find the probability that her height is greater than 63 inches. Express your answer as a decimal using 4 decimal places. Give the exact value from the chart. Do not round your answer.
Sri K.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD