Final answer:
To find the proportion of temperatures between 12.9ºC and 14.9ºC, we need to calculate the z-scores for these temperatures and use them to find the corresponding area under the normal distribution curve. proportion = area2 - area1 = 0.2420 - 0.0446 = 0.1974.
Step-by-step explanation:
To find the proportion of temperatures between 12.9ºC and 14.9ºC, we need to calculate the z-scores for these temperatures and use them to find the corresponding area under the normal distribution curve. The z-score formula is:
z = (x - μ) / σ
where x is the temperature, μ is the mean, and σ is the standard deviation. Plugging in the values for 12.9ºC and 14.9ºC, we get:
z1 = (12.9 - 16.3) / 2 = -1.7
z2 = (14.9 - 16.3) / 2 = -0.7
Next, we need to find the area between these z-scores. We can use a z-table or a calculator to find the corresponding probabilities:
area1 = P(Z < -1.7) = 0.0446
area2 = P(Z < -0.7) = 0.2420
The proportion of temperatures between 12.9ºC and 14.9ºC is the difference between these two probabilities:
proportion = area2 - area1 = 0.2420 - 0.0446 = 0.1974