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tankabanditka
3 months ago
5

Scientists working for a water district measure the water level in a lake each day. The daily water level in the lake varies due

to weather conditions and other factors. The daily water level has a distribution that is approximately normal with mean water level of 84.07 feet. The probability that the daily water level in the lake is at least 100 feet is 0.064. Which of the following is closest to the probability that on a randomly selected day the water level in the lake will be at least 90 feet?
Mathematics
1 answer:
babunello [11.8K]3 months ago
4 0

Answer:

0.2855

Step-by-step explanation:

The mean daily lake water level is M = 84.07 feet.

The probability that the water level is at least 100 feet is given as 0.064, which we write as P(X ≥ 100) = 0.064. For a normal distribution, the corresponding z-score is z = 1.52204.

We use the formula to find the standard deviation s:

z = \frac{X-M}{s}, hence

s = \frac{X-M}{z} = 10.4662

Next, to find P(X ≥ 90), compute the z-score for X = 90:

\frac{90-84.07}{10.4662} = 0.5666

Using this z-value, the probability P(X ≥ 90) equals 0.2855.

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