Its is probability and Statistics Class. I\'m extremely bad with these questions

Question

   Its is probability and Statistics Class. I'm extremely bad with these questions. If you could please write with pencil/pen with work STEP BY STEP, It would be awesome. Please think of it me as a challenged individual because I can't catch when steps are missed. Thank you so much.

Problem 4) Studies show that gasoline use for compact cars sold in the United States is normally distributed with a mean use of 25.5 miles per gallon and a standard deviation of 4.5 miles per gallon. a) What percentage of compacts obtains 30 or more miles per gallon? (6 points) b) If a manufacturer wishes to develop a compact car that outperforms 97.5% of the current compacts in fuel economy, what must be gasoline use for the new car? (6 points)

Explanation / Answer

Mean = 25.5

Sd = 4.5

Z = (X - mean) /sd

A) P(X > 30) = P((X - mean) /sd > (30 - mean) /sd)

= P(Z > (30 - 25.5)/4.5)

= P(Z > 1)

= 1 - P(Z < 1)

= 1 - 0.8413

= 0.1587

= 15.87%

B) P(X > x) = 0.975

Or, P((X - mean) /sd > (x - mean) /sd) = 0.975

Or, P(Z > (x - 25.5)/4.5) = 0.975

Or, 1 - P(Z < (x - 25.5)/4.5) = 0.975

Or, P(Z < (x - 25.5)/4.5) = 0.025

Or, (x - 25.5)/4. 5 = - 1.96

Or, x = 25.5 - 1.96 * 4.5

Or, x = 16.68

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