Question

An instructor is interested in assessing students' typing speed in the class. He knows that the average at the university is 49 word per minute (wpm) with a SD of 18 wpm. He collects data from 31 of his students.

a) What is the probability of the average typing speed being less than 49 wpm?
probability =  

b) What is the proability of the average typing speed being between 51 and 53 wpm?
probability =  

Note: Do NOT input probability responses as percentages; e.g., do NOT input 0.9194 as 91.94.

Answer 1

Let x be the students' typing speed in the class.

We are given mean ( µ ) = 49 and standard deviation (σ) = 18 and n = 31

Therefore according to sampling distribution of sample mean , follows approximately normal distribution with mean ()= 49

and standard deviation = = = 3.2329

Part a) P ( < 49 )

=

= P( z < 0 )

= 0.5000 ------ ( from z score table , value for z= 0 )

Part b) P( 51 ≤ ≤ 53 ) = P( ≤ 53 ) - P( ≤ 51 )

=   

= P( z < 1.24 ) - P( z < 0.62 )

= 0.8925 - 0.7324 ------------ ( from z score table )

= 0.1601