<em>Rearrange unknown terms to the left side of the equation</em>
<em>Calculate the sum or difference.</em>
<em>Convert decimal to fraction.</em>
<em>Reduce the greatest common factor for both sides of the inequality.</em>
<em> </em>
<em>Reduce the fraction</em>
Answer:
a) 0.8413
b) 0.6293
Step-by-step explanation:
Data provided:
Mean tax paid = $2000
Standard deviation = $500
Sample size, n = 625
n=625
Now,
a) P( average tax paid on the sample forms is greater than $1980)
⇒ P(X > 1980)
or
⇒
or
⇒
or
⇒ P(Z > -1)
or
= 0.8413 (From standard normal table)
b) P(more than 60 of the sampled forms have a tax of greater than $3000)
given: p = 10% = 0.1
Now, by using CLT
mean = n × p
= 625 × 0.1
= 62.5
Standard deviation, s =
=
= 7.5
Thus,
P(X > 60)
=
or
= P(Z > -0.33)
= 0.6293 (From standard normal table)