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 $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 ?

Round your answer to three decimal places.

P=???

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

Round your answer to two decimal places.

P=???

Answer 1

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%