The mean temperature during the summer in a certain city is 80 degrees Fahrenheit with a standard deviation of 5 degrees Fahrenheit what is the probability that random selected day has a temperature below 73 degrees
To find the probability that a random selected day has a temperature below 73 degrees, we will first standardize the temperature using the z-score formula:
Z = (X - μ) / σ
where:
- X = temperature we want to find the probability for (73 degrees)
- μ = mean temperature (80 degrees)
- σ = standard deviation (5 degrees)
Plugging in the values, we get:
Z = (73 - 80) / 5
Z = -1.4
Next, we will use a Z-table to find the probability that a temperature is below -1.4 standard deviations from the mean. Looking up the value for Z = -1.4 in the Z-table, we find that the probability is approximately 0.0808.
Therefore, the probability that a random selected day has a temperature below 73 degrees is approximately 0.0808, or 8.08%.