1. Consider the following natality statistics for the US population in 1992. According to these data,...

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1. Consider the following natality statistics for the US population in 1992. According to these data, the probabilities that a randomly selected woman who gave birth in 1992 was in each of the following age groups are as follows: Age Probability <15 0.003 15-19 0.124 20-24 0.263 25-29 0.290 30-34 0.220 35-39 0.085 40-45 0.014 45-49 0.001 Total 1.000 (1) What is the probability that a woman who gave birth in 1992 was 24 years of age or younger? (2) What is the probability that she was 40 or older? (3) Given that the mother of a particular child was under 30 years of age when giving birth in 1992, what is the probability that she was not yet 20? (4) Suppose that two mothers are randomly selected, what is the probability that they were both under 30 years of age when giving birth in 1992? 2. The maximum patent life for a new drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life of the drug-that is, the length of time that a company has to recover research and development costs and make a profit. Suppose the distribution of the lengths of patent life for new drugs is as shown here: Year, x 3 4 5 6 7 8 9 10 11 12 13 p(x) 0.03 0.05 0.07 0.10 0.14 0.20 0.18 0.12 0.07 0.03 0.01 (1) Find the expected number of patent years for a new drug (2) Find the standard deviation of x (3) Find the probability that x falls into the interval 20 3. According to the National Health Survey, 9.8% of the population of 18- to 24-year-olds in the US are left-handed. Suppose you select 10 individuals from this population and x is the number of persons who are left-handed. (1) How many left-handed people are expected to be selected? (2) What is the variance and standard deviation of x? (3) What is the probability that exactly 4 people are left-handed? (4) What is the probability that at least 4 people are left-handed? (5) What is the probability that at most two people are left-handed? (6) Given that at least 4 people are left-handed, what is the probability that exactly 4 are left- handed? 4. Find the following probabilities for the standard normal variable z: (1) P(z <2.33) (2) P(z <1.645) (3) P(z>1.96) (4) P(-2.58 6. The serum cholesterol levels of a certain population of boys follow a normal distribution with mean 176 mg/dl and standard deviation 30 mg/dl. (1) What percentage of the boys have serum cholesterol values 186 or more? (2) What is the probability that a randomly selected boy has a serum cholesterol value 156 or less? (3) What percentage of the boys have serum cholesterol values 216 or less? (4) What percentage of the boys have serum cholesterol values 121 or more? (5) What percentage of the boys have serum cholesterol values between 186 and 216? (6) What is the probability that a randomly selected boy has a serum cholesterol value between 121 and 156? (7) What is the probability that a randomly selected boy has a serum cholesterol value between 156 and 186? (8) How low does a boy's serum cholesterol value have to be so that he is among the lowest 10%? (9) The serum cholesterol value of a boy is 120 mg/dl. Is it unusually low? 1. Consider the following natality statistics for the US population in 1992. According to these data, the probabilities that a randomly selected woman who gave birth in 1992 was in each of the following age groups are as follows: Age Probability <15 0.003 15-19 0.124 20-24 0.263 25-29 0.290 30-34 0.220 35-39 0.085 40-45 0.014 45-49 0.001 Total 1.000 (1) What is the probability that a woman who gave birth in 1992 was 24 years of age or younger? (2) What is the probability that she was 40 or older? (3) Given that the mother of a particular child was under 30 years of age when giving birth in 1992, what is the probability that she was not yet 20? (4) Suppose that two mothers are randomly selected, what is the probability that they were both under 30 years of age when giving birth in 1992? 2. The maximum patent life for a new drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life of the drug-that is, the length of time that a company has to recover research and development costs and make a profit. Suppose the distribution of the lengths of patent life for new drugs is as shown here: Year, x 3 4 5 6 7 8 9 10 11 12 13 p(x) 0.03 0.05 0.07 0.10 0.14 0.20 0.18 0.12 0.07 0.03 0.01 (1) Find the expected number of patent years for a new drug (2) Find the standard deviation of x (3) Find the probability that x falls into the interval 20 3. According to the National Health Survey, 9.8% of the population of 18- to 24-year-olds in the US are left-handed. Suppose you select 10 individuals from this population and x is the number of persons who are left-handed. (1) How many left-handed people are expected to be selected? (2) What is the variance and standard deviation of x? (3) What is the probability that exactly 4 people are left-handed? (4) What is the probability that at least 4 people are left-handed? (5) What is the probability that at most two people are left-handed? (6) Given that at least 4 people are left-handed, what is the probability that exactly 4 are left- handed? 4. Find the following probabilities for the standard normal variable z: (1) P(z <2.33) (2) P(z <1.645) (3) P(z>1.96) (4) P(-2.58 6. The serum cholesterol levels of a certain population of boys follow a normal distribution with mean 176 mg/dl and standard deviation 30 mg/dl. (1) What percentage of the boys have serum cholesterol values 186 or more? (2) What is the probability that a randomly selected boy has a serum cholesterol value 156 or less? (3) What percentage of the boys have serum cholesterol values 216 or less? (4) What percentage of the boys have serum cholesterol values 121 or more? (5) What percentage of the boys have serum cholesterol values between 186 and 216? (6) What is the probability that a randomly selected boy has a serum cholesterol value between 121 and 156? (7) What is the probability that a randomly selected boy has a serum cholesterol value between 156 and 186? (8) How low does a boy's serum cholesterol value have to be so that he is among the lowest 10%? (9) The serum cholesterol value of a boy is 120 mg/dl. Is it unusually low?