Help with homework question?

In order to ride in a car at the Tomorrowland Speedway at Magic Kingdom, you must be at least 32 inches tall. To drive a car at the Tomorrowland Speedway, you must be at least 54 inches tall. Assume 5th graders heights are normally distributed. The mean height for female 5th graders is 54.4 inches with a standard deviation of 2.7 inches. The mean height for male 5th graders is 55.5 inches with a standard deviation of 2.7 inches. For each of the following, draw a sketch of the situation, shade the appropriate area, and round your percentage to the nearest hundredths.

a. What percent of 5th grade boys can drive a car at the Tomorrowland Speedway?








b. What percent of 5th grade girls can drive a car at the Tomorrowland Speedway?









If the creators of the Tomorrowland Speedway want to change the height requirement to allow the tallest 90% of 5th grade boys to drive a car, what should the new height requirement be?

 

Those are relatively straight forward problems IF you are taking a statistics class (If not, where did you get these problems!).

You will need a table or graph of the "standard normal distribution". There is one at
standard normal distribution table - Bing images.

You have, for females, mean mu= 54.4 inches and standard deviation sigma= 2.7 inches and, for males, mean mu= 55.5 inches standard deviation, sigma= 2.7.

For boys the 55.5 inch requirement to drive corresponds to the "standard normal" value (55.5- 54)(2.7)= 0.555. On the table 0.555 has probability 0.2065 (halfway between 0.2008 and 0.2123). Since that is positive and the mean has probability 1, the probability a boy can drive is 0.5+ 0.2065= 0.7065.

For the girls the 54 inch requirement corresponds to "standard normal" value (54.4- 54)(2.7)= 0.1481. On the table, 0.1481 has probability 0.0596. The probability a girl can drive is 0.5+ 0.0596= 0.5596.

The other problems are done in the same way.