Binomial and Normal distributions 1.Yesterday the proportion of all stocks that had gains was 0.74. You own 10 stocks. What is the
Please show all the work step by step thank you Please find attached solution of your assignment. Regards • 1.Yesterday the proportion of all stocks that had gains was 0.74. You own 10 stocks. What is the probability that more than 7 of your stocks had gains? Answer: We have n = 10, p = 0.74 and x = 7 Using binomial distribution, P [X > 7] = P[X = 8] + P [X = 9] + P [X = 10] = 0.2735 + 0.1730 + 0.0492 = 0.4957 2. Clyde hits 70% of his free throws in basketball. Determine the probability that Clyde makes 8 out of 14 free throws. Answer: We have n = 14, p = 0.70 and x = 8 Using binomial distribution, P [X = 8] = 14C8 (0.70)^8 (0.30)^6 = 0.1262 3. The random number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a Uniform Probability Distribution. What is the probability of generating a number between 0 and 0.2? Answer: P (0 ≤ X ≤ 2) = (x – a)/ (b – a) = (0.2 – 0)/ (1 – 0) = 0.2 4. Suppose that combined verbal and math SAT scores follow a normal distribution with mean 896 and standard deviation 174. Suppose further that Peter finds out that he scored in the top 3% of SAT scores. Determine how high Peter’s score must have been. Answer: We have µ = 896 and σ = 174 The respective Zscore with p > 0.03 is 1.88 Z = (X µ)/σ 1.88 = (X – 63.5)/2.5 1.88 x 2.5 + 63.5 = X X = 68.2 5. Heights of adult women in the United States are normally distributed with a population mean of µ =63.5 inches and a population standard deviation of σ = 2.5. A medical researcher is planning to select a large random sample of adult women to participate in a future study. What percentage of the women in the researcher’s sample would you expect to have a height of 68.5 inches or LESS? Answer: We have µ = 63.5 and σ = 2.5 The respective Zscore with X = 68.5 is Z = (X µ)/σ = (68.5 – 63.5)/2.5 = 2 Using Ztables, P [Z ≤ 2] = 1 – 0.0228 = 0.9772 or 97.72%
1.Yesterday the proportion of all stocks that had gains was 0.74. You own 10 stocks. What is the
probability that more than 7 of your stocks had gains?
2. Clyde hits 70% of his free throws in basketball. Determine the probability that Clyde makes 8 out of 14 free throws.
3.The random number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a Uniform Probability Distribution. What is the probability of generating a number between 0 and 0.2?
4. Suppose that combined verbal and math SAT scores follow a normal distribution with mean 896 and standard deviation 174. Suppose further that Peter finds out that he scored in the top 3% of SAT scores. Determine how high Peter’s score must have been.
5.Heights of adult women in the United States are normally distributed with a population mean of =
63.5 inches and a population standard deviation of = 2.5. A medical researcher is planning to select a large random sample of adult women to participate in a future study.
What percentage of the women in the researcher’s sample would you expect to have a height of 68.5 inches or LESS?
Answer & Explanation
OR