Probability of normal distribution: average daily temperature - interpretationThe City of Dallas has records indicating that the average daily temperature in the summer is 80 °F, which is normally distributed with a standard deviation of 3 °F.Based on these records, what is the probability of a daily temperaturebetween 75 °F and 87 °Fbetween 83 °F and 85 °F P ( X &lt; 75 ) = P ( Z &lt; − 5 / 3 ) = 0.0485 P ( X &lt; 87 ) = P ( Z &lt; 7 / 3 ) = 0.9901 P ( X &lt; 83 ) = P ( Z &lt; 1 ) = 0.8413 P ( X &lt; 85 ) = P ( Z &lt; 5 / 3 ) = 0.9515Am I following the right steps?How do I interpret my data?

Question

Probability of normal distribution: average daily temperature - interpretationThe City of Dallas has records indicating that the average daily temperature in the summer is 80 °F, which is normally distributed with a standard deviation of 3 °F.Based on these records, what is the probability of a daily temperaturebetween 75 °F and 87 °Fbetween 83 °F and 85 °F  P  (  X  &amp;lt;  75  )  =  P  (  Z  &amp;lt;  −  5      /    3  )  =  0.0485  P  (  X  &amp;lt;  87  )  =  P  (  Z  &amp;lt;  7      /    3  )  =  0.9901  P  (  X  &amp;lt;  83  )  =  P  (  Z  &amp;lt;  1  )  =  0.8413  P  (  X  &amp;lt;  85  )  =  P  (  Z  &amp;lt;  5      /    3  )  =  0.9515Am I following the right steps?How do I interpret my data?

poquetahr · Accepted Answer

You&#039;re on the right track. All that remains for you is to note that  P  (  a  ≤  X  ≤  b  )  =  P  (  X  ≤  b  )  −  P  (  X  ≤  a  )and that this holds for any continuous distribution X, including the standard normal distribution Z.

Probability of normal distribution: average daily temperature - interpretation The City of Dallas h

Answered question

Answer & Explanation

New Questions in Pre-Algebra