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Crickets The length in inches of a cricket chosen at random from a field is a random
Chapter 6, Problem 35(choose chapter or problem)
Crickets The length in inches of a cricket chosen at random from a field is a random variable X with mean 1.2 inches and standard deviation 0.25 inches. Find the mean and standard deviation of the length Y of a randomly chosen cricket from the field in centimeters. There are 2.54 centimeters in an inch.
Questions & Answers
QUESTION:
Crickets The length in inches of a cricket chosen at random from a field is a random variable X with mean 1.2 inches and standard deviation 0.25 inches. Find the mean and standard deviation of the length Y of a randomly chosen cricket from the field in centimeters. There are 2.54 centimeters in an inch.
ANSWER:
Step 1 of 3
Define a random variable \(X\) for length of cricket in inches.
The mean is 1.2 inches.
The standard deviation is 0.25 inches.
That is,
\(\begin{aligned} \mu_{x} & =1.2 \\ \sigma_{x} & =0.25 \end{aligned}\)
The formula for mean and standard deviation is,
\(\begin{aligned} \mu_{x} & =\frac{\sum x_{i}}{n} \\ \sigma_{x} & =\sqrt{\frac{\sum\left(x_{i}-\mu_{x}\right)^{2}}{n}} \end{aligned}\)