Question

Inferential Statistics Ideas 85 ose commuters' one-way distances to work have a mean of 15.41 miles with standard deviation 17.3 miles. a) If 235 commuters are randomly selected, what is the probability that their mean commute distance is between 15.67 miles and 18.84 miles? b) If three commuters are randomly selected, what is the probability that their mean commute distance is less than 36.78 miles?

Answer 1

Hen, na 3 I7.3 V 3 17-3 normed tarble) ー) 0:9833 probabnity that the. Y mean commute distante is less than 3678 miles、

Answer 2

SOLUTION :

Mean, m = 15.41 miles

SD, s = 17.3 miles,

Sample size, n = 235 

a.

SD of distribution of sample means 

= s / sqrt (n)   (n is sample size)

= 17.3 /sqrt(235)

= 1.1285

Sample mean = population mean = m = 15.41

So,

P( 15.67 ≤  m ≤ 18.84) 

= P( (15.67 - 15.41) / 1.1285 ≤ z ≤ (18.84 - 15.41)/1.1285)

= P (0.2304 ≤ z ≤ 0.3.0394)

=> P( z < 3.0394) - P(z < 0.2304)

= 0.9988 - 0.5911

= 0.4077 (ANSWER) 

b. 

n = 3

SD of distribution of sample means = s / sqrt (n) = 17.3/sqrt(3) = 9.9882

So,

P( m < 36.78)

= P(z < (36.78 - 15.41)/9.9882)

= P(z < 2.1395)

= 0.9838 (ANSWER)