Question

1. Suppose that for Edwardsville High School, distances between students’ homes and the high school observe normal distribution with the average distance being 4.76 miles and the standard deviation being 1.74 miles. Express distances and z scores to two decimal places. Write the formula to be used before each calculation.

1d. Suppose all samples of size 12 are taken. What percentage of sample means has a value larger than 6.78 miles?

Answer 1

X ~ N ( µ = 4.76 , σ = 1.74 )  
P ( X̅ > 6.78 ) = 1 - P ( X < 6.78 )   
Standardizing the value   
Z = ( X - µ ) / ( σ / √(n))  
Z = ( 6.78 - 4.76 ) / ( 1.74 / √ ( 12 ) )  
Z = 4.02  
P ( ( X - µ ) / ( σ / √ (n)) > ( 6.78 - 4.76 ) / ( 1.74 / √(12) )  
P ( Z > 4.02 )   
P ( X̅ > 6.78 ) = 1 - P ( Z < 4.02 )   
P ( X̅ > 6.78 ) = 1 - 1  
P ( X̅ > 6.78 ) = 0%