Question

Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. Use this distribution for the following questions about height.

What is the probability that a randomly chosen 10 year old is shorter than 48 inches?

5 points   

QUESTION 19

What is the probability that a randomly chosen 10 year old is between 60 and 65 inches?

5 points   

QUESTION 20

If the tallest 10% of the class is considered “very tall”, what is the height cutoff for “very tall”?

5 points   

QUESTION 21

The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What percent of 10 year olds cannot go on this ride?

Please answer as a percentage for this problem ( 0 to 100). Do not include the % sign.

Answer 1

Solution:

= 55

= 6

( 18 )

P( x < 48 ) = P( z < ( 48 - 55 ) / 6 )

= P( z < -1.1666 )

= 0.1210

( 19 )

P( 60 < x < 65 ) = P( ( 60 - 55 )/6 < z < ( 65 - 55 ) / 6 )

= P( 0.8333 < z < 1.6666 )

= P( z < 1.6666 ) - P( z < 0.8333 )

= 0.9525 - 0.7967

= 0.1558

( 20 )

let the cutoff value be x

z score for top 10% = 1.2815

we know that

z = ( x - ) /

1.2815 = ( x - 55 )/ 6

x - 55 = 7.689

x = 62.689

( 21 )

P( x < 54 ) = P( z < (54-55)/ 6 )

= P( z < -0.1666)

= 0.4325

Percentage of 10 year olds cannot go on this ride = 43.25