Question

# The Bank of Connecticut issues Visa and MasterCard credit cards. It is estimated that the balances...

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

(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