We did not find results for: High temperatures in a certain city for the month of August follow a uniform distribution over the interval 69*F to 87*F. what is the probability that a randomly selected August day has a high temperature that exceeded 74*F?.

.72222

(87-74)/(87-69) = ?

To find the probability that a randomly selected August day has a high temperature that exceeds 74°F, we need to calculate the area under the probability density function (PDF) curve for temperatures greater than 74°F.

Given that the high temperatures in the city for the month of August follow a uniform distribution over the interval 69°F to 87°F, we can determine the width of the interval as:

Width = Maximum temperature - Minimum temperature
Width = 87°F - 69°F
Width = 18°F

The uniform distribution has a constant probability density over the interval, so the height of the PDF curve is:

Height = 1 / Width
Height = 1 / 18°F

To find the probability that the temperature exceeds 74°F, we need to calculate the area under the PDF curve from 74°F to 87°F. The width of this interval is:

Width = 87°F - 74°F
Width = 13°F

The probability is given by the product of the height of the PDF curve and the width of the interval:

Probability = Height * Width
Probability = (1 / 18°F) * 13°F
Probability ≈ 0.7222

Therefore, the probability that a randomly selected August day has a high temperature that exceeds 74°F is approximately 0.7222 or 72.22%.

To find the probability that a randomly selected August day has a high temperature that exceeds 74°F, we can use the concept of uniform distribution.

Given information:
- High temperatures in a certain city for the month of August follow a uniform distribution over the interval 69°F to 87°F.
- We want to find the probability that the temperature exceeds 74°F.

To solve this problem, we need to calculate the proportion of the interval between 74°F and 87°F relative to the total interval between 69°F and 87°F. This will give us the probability of the temperature exceeding 74°F.

Step 1: Calculate the total width of the interval
The total width of the interval is calculated by subtracting the lower limit from the upper limit:
Total width = 87°F - 69°F = 18°F

Step 2: Calculate the width of the subinterval
The width of the subinterval from 74°F to 87°F is calculated by subtracting the lower limit from the upper limit:
Subinterval width = 87°F - 74°F = 13°F

Step 3: Calculate the probability
The probability of the temperature exceeding 74°F is the ratio of the subinterval width to the total interval width:
Probability = (Subinterval width) / (Total width)

Plugging in the values:
Probability = 13°F / 18°F ≈ 0.7222

Therefore, the probability that a randomly selected August day has a high temperature that exceeds 74°F is approximately 0.7222, or 72.22%.