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?

The probability that the daily water level in the lake is at least 100 feet is 0.064. We can write it as P(X≥100)=0.064 In a normal distribution corresponding z-score of X to this probability is z= 1.52204

From here, standart deviation of the distribution s can be found by using the formula:

z= [tex]\frac{X-M}{s}[/tex] i.e

s= [tex]\frac{X-M}{z}[/tex] = 10.4662

For P(X≥90), we can calculate z-score of X:

[tex]\frac{90-84.07}{10.4662}[/tex] =0.5666

Using this z value P(X≥90) = 0.2855