Question

Among the income-tax forms filed in a certain year, the mean tax paid was $2,000 and the standard

deviation was $500. A random sample of 625 forms is drawn. Let X be the mean tax paid on the sample

of 625 forms.

a. What will you use for the distribution of X , including any parameters? Explain!!!

b. What is the probability that the mean tax paid on the sample forms is greater than

$1,980?

Answer 1

Solution :

Given that ,

mean = = $2000

standard deviation = = $500

n = 625

= 2000

= / n = 500/ 625 = 20

P( >1980 ) = 1 - P( <1980 )

= 1 - P[( - ) / < (1980-2000) /20 ]

= 1 - P(z <-1 )

Using z table

= 1 - 0.1587

= 0.8413

probability= 0.8413

Solution