Suppose that the random variable X has a geometric distribution with a p = 0.4. Calculate the following: a. P(X = 2) b. Р(X < 5) c. Evaluate the mean, variance and standard deviation.
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- A population has a mean of 200 and a standard deviation of 90. Suppose a simple random sample of size 125 is selected and is used to estimate μ. Use z-table. a. What is the probability that the sample mean will be within 18 of the population mean (to 4 decimals)? b. What is the probability that the sample mean will be within 16 of the population mean (to 4 decimals)?For the population of one town, the number of siblings, x, is a random variable whose relative frequency histogram has a reverse J-shape. The mean number of siblings is 1.3 and the standard deviation is 1.5. Let x denote the mean number of siblings for a random sample of size 32. Determine whether the distribution of x is normal or approximately normal and find its mean and standard deviation.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
- Assume that final exam scores in a given course are approximately normally distributed with a mean of 75 and a standard deviation of 10 points. In a class of 200 students, how many would you expect to fail the exam (i.e., score less than 60) (note: scores can only be approximately normally distributed, because the minimum score is 0, but this should not alter the answer, given how large the mean is relative to the standard deviation).Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 6.5752 7.3865 is the standard deviation of the second sample.Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. College A 3.7 3.2 3.0 2.5 2.7 3.6 2.8 3.4 College B 3.8 3.2 3.0 3.9 3.8 2.5 3.9 2.8 4.0 3.6 2.6 4.0 3.6 Construct a 95% confidence interval for μ1−μ2, the difference between the mean GPA of college A students and the mean GPA of college B students. Round to two decimal places. (Note: x1=3.1125, x2=3.4385, s1=0.4357 s2=0.5485
- Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 3.96014.5373 is the standard deviation of the second sample.Assume that X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the following: a. P(Z < 13) b. P(Z > 9) c. P(6 < X < 14)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 shape of the sampling distribution of ? Normal because both population distributions are Normal uniform because the both sample sizes are less than 30 skewed right because the difference in times cannot be negative skewed left because the sample sizes are less than 30 and the sampling variability is unknown
- Q3: The effective life of a component used in a jet-turbine aircraft engine is a random variable with mean 5000 hours and standard deviation 40 hours. The distribution of effective life is fairly close to a normal component that increases the mean life to 5030 hours and decreases the standard deviation to 30 hours. distribution. The engine manufacturer introduces an improvement into the manufacturing process for this Suppose that a random sample of n₁ = 16 components is selected from the "Old" process and a random sample of n₂ = 25 components is selected from the "Improved" process. What is the probability that difference in the two-sample means that the old and improved processes can be regarded as independent populations. 5 X₂X₁ is at least 15 hours? AssumeSuppose that the weights of adult males have a mean of 60kls and standard deviation of 18 kg. Suppose that the distribution of weights is not normal and n = 40. Find the probability that a random sample of 15 males will have a mean weight that exceeds 75kg. .9998 0.0002 0.2 0.0001 Other:Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 2.44628.0027 is the standard deviation of the second sample.