Question

очень срочно!!!Математическое ожидание веса зерна равно 0,2 г, среднее квадратическое отклонение равно 0,05 г. найти вероятность того, что вес наудачу взятого зерна отклоняется от среднего значения не более чем на 0,02

Answer 1

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Answer 2

Calculation of Probability

To find the probability that the weight of a randomly selected grain deviates from the mean by no more than 0.02 grams, we can use the concept of the standard normal distribution.

The formula for calculating the probability is:

P(|X - μ| ≤ σ) = Φ((X - μ) / σ)

Where: - P is the probability - X is the random variable (weight of the grain) - μ is the mean (0.2 grams) - σ is the standard deviation (0.05 grams) - Φ is the cumulative distribution function of the standard normal distribution

Substituting the given values into the formula, we have:

P(|X - 0.2| ≤ 0.05) = Φ((X - 0.2) / 0.05)

To calculate this probability, we need to find the z-score, which represents the number of standard deviations away from the mean the value is. The z-score is calculated as:

z = (X - μ) / σ

In this case, we want to find the probability that the z-score is less than or equal to 0.4 (0.02 / 0.05).

Using a standard normal distribution table or a statistical software, we can find the corresponding probability.

Let's calculate it step by step.

1. Calculate the z-score: z = (0.02 - 0.2) / 0.05 = -3.6

2. Look up the probability corresponding to the z-score of -3.6 in the standard normal distribution table or use statistical software.

According to the standard normal distribution table, the probability corresponding to a z-score of -3.6 is approximately 0.0002.

Therefore, the probability that the weight of a randomly selected grain deviates from the mean by no more than 0.02 grams is approximately 0.0002.

Please note that the actual probability may vary slightly depending on the level of precision used in the calculations.