A random sample of size ₁ = 16 is selected from a normal population with a mean of 75 and a standard deviation of 8. A second random sample of size n2 = 9 is taken from another normal population with mean 70 and standard deviation 12. Let X₁ and X₂ be the two sample means. Find: (a) The probability that X₁ X₂, exceeds 4 (b) The probability that 3.5 ≤ X₁ – X₂ ≤ 5.5 -
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- A company manufactures tonnis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 54.7 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between -to ak and t as then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.8 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Find -th os and to 96- -to.96 = 0.96 = (Round to three decimal places as needed.)Let the random variable x have a normal distribution with a mean value of 70 and a varience of 25. Then find the probability that P (x<80)Use the Suppose in a local Kindergarten through 12th grade (K -12) school district, 42% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. nd the mean and the standard deviation of X of B(144, 0.42). Round off to 4 decimal places. b. Now approximate X of B(144, 0.42) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y N( C Find the probability that at most 72 favor a charter school using the normal approximation and the table. Round off to z-values up to 2 decimal places.) P(X 68) P(Y > ~ (Z >) e. Find the probability that exactly 63 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 63) P(
- a) Find such that P( X < ? ) = 0.9332, where X is a normal random variable with mean = 10 and standard deviation = 2.5. b) Find such that P( X > ?) = 0.1230, where X is a normal random variable with mean = 10 and standard deviation = 2.5.Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. A. What is the variance of the sample mean Xn? B. Use your answer to part (A), and Chebyshev’s inequality, to come up with a quantitative upper bound for the probability that sample mean Xn is more than a certain distance of 175Assume that the random variable X is normally distributed with mean = 15 and standard deviation = 2. Let n = 4. Find P( > 16) and P( < 16).
- where appropriate. 1. Experience has shown that the seeds from a certain variety of orchid have a 75% chance of germinating when planted under normal conditions. Suppose n seeds are planted, and let X be the random variable that counts the number of seeds that germinate. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) = = (b) What is the minimum value of n so that the probability of at least five of the seeds germinating is at least 90%?An IQ test is designed so that the mean is 100 and the standard deviation is 14 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 4 IQ points of the true mean. Assume that σ=14 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn, without burning it, are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the mean of the sampling distribution of ? A) –50 B) 50 C) 90 D) 140
- Carboxyhemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood.t Let x be a random variable representing percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n = 12 blood tests given to a heavy smoker gave the following results (percent carboxyhemoglobin in the blood). Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. 9.1 9.8 10.4 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 (a) Use your calculator to calculate x and s. (Round your answers to four decimal places.) X = S = (b) A long-term population mean u = 10% is considered a health risk. However, a long-term population mean above 10% is considered a…Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, µ, spent by customers at the supermarkets has been reported to be 40 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 40 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 44 minutes and the standard deviation of the times to be 15 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? Hiµ is ? H: p is ? In the context of this test, what is a Type II error? A Type II error is ? fact, u is ? the hypothesis that u is when, in Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making?Assume that women's weights are normally distributed with a mean given by μ=143 lb and a standard deviation given by 29 lb.(a) If 1 woman is randomly selected, find the probabity that her weight is between 113 lb and 172 lb(b) If 3 women are randomly selected, find the probability that they have a mean weight between 113 lb and 172 lb(c) If 73 women are randomly selected, find the probability that they have a mean weight between 113 lb and 172 lb
