1. the engines made by Alpha-X for boats have an average power of 220 horsepower (HP) and a standard deviation of 15 HP. You can assume the distribution of power follows a normal distribution. Beta-Y is testing the engines and will dispute the company's claim if the simple mean is less than 215 HP. if they take a sample of 4 engines. A. what is the probability the mean is less than 215? B. If Beta-Y samples 100 engines, what is the pribability that the sample mean will be less than 215?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. the engines made by Alpha-X for boats have an average power of 220 horsepower (HP) and a standard deviation of 15 HP. You can assume the distribution of power follows a normal distribution. Beta-Y is testing the engines and will dispute the company's claim if the simple mean is less than 215 HP. if they take a sample of 4 engines.

A. what is the probability the mean is less than 215?

B. If Beta-Y samples 100 engines, what is the pribability that the sample mean will be less than 215?

2. the weights of baby kangaroos are known to have a mean of 125 pounds and a standard deviation of 15 pounds. if we obtained a random sample of 40 baby kangaroos.

A. what is the probability that the sample mean will be between 120 and 130 pounds?

B. what are the confidence intervals having the same number of samples with a 95% confidence level?

3. we heard that there was a 90% confidence interval for the population mean from 22.5 to 28.3, determine 

A. the point estimate of the population

B. the margin of error associated with the information

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