While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. what is the probability that a randomly selected depth is within 1 standard deviation of the mean?

The probability that a randomly selected depth is within one standard deviation of the mean .

Further Explanation:

Given:

A marine biologist selects water depths from a uniformly distributed collection between and .

Explanation:

The depth follows uniform distribution with upper limit 7 and lower limit 2.

Here, is the mean, is the lower limit and is the upper limit.

The mean can be calculated as follows,

The standard deviation of the depth can be calculated as follows,

The probability density function can be obtained as follows,

The probability that a randomly selected depth is within 1 standard deviation of the mean can be expressed as,

Here, represents the mean and represents the standard deviation.

The probability that a randomly selected depth is within 1 standard deviation of the mean can be calculated as follows,

The probability that a randomly selected depth is within one standard deviation of the mean .

Learn more:

1. Learn more about normal distribution

2. Learn more about standard normal distribution

3. Learn more about confidence interval of mean

Answer details:

Grade: College

Subject: Statistics

Chapter: Confidence Interval

Keywords: Z-score, Z-value, marine biologist, experiments, binomial distribution, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, uniformly distributed.

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