Statistics Question

Question

Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.

 

 

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

(b) What is the probability that a randomly chosen 10 year old is between 58 and 66 inches?

(c) If the tallest 5 % of the class is considered “very tall”, what is the height cutoff for “very tall”?

(d) 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?

Answer 1

a) 12.167 % chance

calculate z =(48-55)/6 then use z tables

b) (58-55)/6 = 3/6 = .5, (66-55)/6 = 11/6 = about 1.8333

use z tables to find areas under the normal curve, then subtract

.4667 - .1915 = .2752= about 27.52 % chance between 58 and 66 inches

c) cut off for top 5%, area under the normal curve from z= 0 to z= ? when z tables show .45 area under the curve. z= 1.645 = (x-55)/6 solve for x

x-55 = 6(1.645)

x = 55 + 9.87= 64.87 inches is very tall

d) (54-55)/6 = 1/6 = -.16666... find area under the curve to the left of that z score Use z tables.

.43382 = 43.382% can't go on the ride