Question

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= ___________%

Answer #1

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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