A set of average city temperatures in July are normally distributed with a mean of $23.5^{\circ} \mathrm{C}$ and a standard deviation of $2^{\circ} \mathrm{C}$. The average temperature of Rabat is $23^{\circ} \mathrm{C}$.

What proportion of average city temperatures are higher than that of Rabat?
You may round your answer to four decimal places.

Question

A set of average city temperatures in July are normally distributed with a mean of $23.5^{\circ} \mathrm{C}$ and a standard deviation of $2^{\circ} \mathrm{C}$. The average temperature of Rabat is $23^{\circ} \mathrm{C}$.

What proportion of average city temperatures are higher than that of Rabat?
You may round your answer to four decimal places.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the z-score for Rabat's average temperature. ‖ ‖ step 2 ⋮ The z-score is calculated using the formula $z = \frac{X - \mu}{\sigma}$, where $X$ is Rabat's temperature, $\mu$ is the mean temperature, and $\sigma$ is the standard deviation. ‖ ‖ step 3 ⋮ Substituting the given values, we get $z = \frac{23 - 23.5}{2} = -0.25$. ‖ ‖ step 4 ⋮ Look up the z-score in the standard normal distribution table or use a calculator to find the proportion of the area to the right of this z-score. ‖ ‖ step 5 ⋮ The area to the right of $z = -0.25$ corresponds to the proportion of average city temperatures higher than that of Rabat. ‖ ‖ step 6 ⋮ Using the standard normal distribution table or a calculator, we find that the area to the right of $z = -0.25$ is approximately 0.5987. ‖ ∻Answer∻ ⚹ The proportion of average city temperatures higher than that of Rabat is approximately 0.5987. ⚹ ∻Key Concept∻ ⚹Z-score and Normal Distribution⚹ ∻Explanation∻ ⚹The z-score represents the number of standard deviations a data point is from the mean. In a normal distribution, the area to the right of a negative z-score represents the proportion of data points that are higher than the given value◊What is the formula to calculate the z-score for a given value in a normal distribution?⍭ Generate me a similar question◊⚹

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