Final answer:
To find the probability P(x ≥ 2) when x has a normal distribution with a mean of 2.7 and a standard deviation of 0.37, we can calculate the z-score for x = 2, and then use a standard normal distribution table or calculator to find the probability associated with that z-score.
Step-by-step explanation:
To find the probability P(x ≥ 2) when the value of x is normally distributed with a mean (μ) of 2.7 and a standard deviation (σ) of 0.37, we need to calculate the area under the curve to the right of x = 2.
We can calculate this probability by finding the z-score for x = 2 using the formula z = (x - μ) / σ, and then using a standard normal distribution table or calculator to find the probability associated with that z-score.
In this case, the z-score for x = 2 is z = (2 - 2.7) / 0.37 = -1.89 (rounded to two decimal places).
Using a standard normal distribution table or calculator, we can find that the probability P(z ≥ -1.89) is approximately 0.9702 (rounded to four decimal places).
Therefore, the probability P(x ≥ 2) is approximately 1 - 0.9702 = 0.0298 (rounded to four decimal places).
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