Answer:
- 0.98 approximately
- 0.25 approximately
- 0.34 approximately
Explanation:
standard deviation by which debt is distributed = $1100
average credit card debt for college seniors = $3262
A) probability that senior owes at least $1000
P (x ≥ 1000 ) = P ( Z ≥ )
where = $3262
= $1100
Z = random variable representing credit card debt for college seniors
back to equation P ( Z ≥ )
therefore P ( z ≥ -2.06 )
1 - p ( z ≤ -2.06 )
therefore probability of the senior owing $1000 = 1 - 0.0199 = 0.9801
B) probability that senior owes more than $4000
p ( x ≥ 4000) = P ( Z ≥ )
= P ( Z ≥ )
= 1 - p ( Z ≤ 0.67 ) therefore probability that senior owes more than $4000 = 1 - 0.7468 = 0.2514
C ) Probability that the senior owes between $300 and $4000
P ( 3000 ≤ x ≤ 4000) = P ( ≤ Z ≤
)
= P ( ≤ z ≤
)
= P ( - 0.24 ≤ z ≤ 0.67 )
= p ( z ≤ 0.67 ) - p ( z ≤ - 0.24 )
= 1 - p ( z ≥ 0.67 ) - 1 - p ( z ≥ -0.24 )
= 0.7846 - 0.4052 = 0.3434