Given X is a normally distributed random variable with a mean of 155 and a standard deviation of 11.6, determine a) P(X>170) b) P(152
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Given X is a
a) P(X>170) b) P(152<X<170)
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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)?2) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probabilities. (Tips: Find the value for z; then, use the table) a) P(x 92); µ = 85; o = 8 c) P(16< x < 22); µ = 15; o = 4Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, u, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate u. Assuming that the standard deviation of the population of shopping times at the supermarkets is 27 minutes, what is the minimum sample size she must collect in order for her to be 99% confident that her estimate is within 5 minutes of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) ?
- Assume that X has a normal distribution, and find the indicated probability. 7) The mean is μ = 15.2 and the standard deviation is o = 0.9. Find the probability that X is between 14.3 and 16.1. A) 0.1587 B) 0.6826 C) 0.8413 D) 0.3413 7)Let the weights of 1 kg tea boxes filled with an automatic machine have a normal distribution with a mean of μ=1.03 and a standard deviation of σ=0.02 kg.a) What is the probability that any tea box will weigh less than 1 kg?b) What is the probability that any tea box will weigh higher than 1,06 kg?1. The standard deviation of SAT scores is 100 points. A researcher decides to take a sample of 500 students’ scores to estimate the mean score of students in your state. What is the standard deviation of the sample mean? A) 0.2 B) 5 C) 4.47 D) 100 2. a binomial distribution with n = 10 and p = 0.2 . P(X = 5)= A) 0.34 B) 0.021 C) 0.026 D) 0.41
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