The Bank of Connecticut issues Visa and MasterCard credit cards.
It is estimated that the balances on all Visa credit cards issued
by the Bank of Connecticut have a mean of $830 and a standard
deviation of $275. Assume that the balances on all these Visa cards
follow a normal distribution.
a. What is the probability that a randomly
selected Visa card issued by this bank has a balance between $950
and $1400?
Round your answer to three decimal places.
P=
b. What percentage of the Visa cards issued by
this bank have a balance of $735 or more?
Round your answer to two decimal places.
P= ___________%
Solution :
Given that ,
mean = = $830
standard deviation = = $275
P($950< x <$1400 ) = P[(950 - 830) /275 < (x - ) / < (1400 - 830) /275 )]
= P( 0.44< Z < 2.07)
= P(Z <2.07 ) - P(Z < 0.44)
Using z table,
= 0.9808 - 0.6700
=0.3108
answer =0.311
(B)
P(x > $735) = 1 - P(x <735 )
= 1 - P[(x- ) / < (735 - 830) /275 ]
= 1 - P(z < -0.35)
Using z table,
= 1 - 0.3632
=0.6368
answer =63.68%
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