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 \$850 and a standard deviation of \$265. 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 \$1000 and \$1410 ?

P=???

B. What percentage of the Visa cards issued by this bank have a balance of \$725 or more?

P=???

Solution :

Given that ,

mean = = \$850

standard deviation = = \$265

A.

P(\$1000 < x < \$1410) = P[(1000 - 850)/ 265) < (x - ) /  < (1410 - 850) / 265) ]

= P(0.5660 < z < 2.1132)

= P(z < 2.1132) - P(z < 0.5660)

= 0.9827 - 0.7143

= 0.268

Probability = 0.268

B.

P(x \$725) = 1 - P(x   725)

= 1 - P[(x - ) / (725 - 850) / 265]

= 1 -  P(z -0.4717)

= 1 - 0.3186

= 0.6814

percentage = 68.14%

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