The bank of connecticut issues visa and mastercard credit cards. the balances on these credit cards follow a normal distribution with a mean of $845 and standard deviation of $270. what percentage of balances is between $600 and $1,000?

53.37% of balances are between $600 and $1000

Step-by-step explanation:

Lets call X the balance of a cradit card. X is a normal distribution with mean 845 and standard deviation of 270.

We can standardize X so that it has distribution equal to the standard normal distribution. For that consider Z = (X-845)/270. Z is a standard normally distributed random variable.

We want to calculate P( 600 < X < 1000). That is the same as calculate P( (600-845)/270 < Z < (1000-845)/270) = P(-0.907 < Z < 0.574)

Remember that for a value of k we have that P(Z < k) = Φ(k), where Φ denotes the cummulative distribution function of a standard normal random variable. The values of Φ can be found on the table i attached with this answer.  

P(-0.907 < Z < 0.574) = P(Z < 0.574) - P(Z < -0.907) = Φ(0.574)-Φ(-0.907)

We can read the table to obtain that Φ(0.574) = 0.7157. To calculate Φ(-0.907) we can use the simetry of the normal function (on the y axis) to conlcude that Φ(-0.907) = 1 - Φ(0.907) = 1 - 0.8186 = 0.1814.

Finally P( 600 < X < 1000) = Φ(0.574)-Φ(-0.907) = 0.7157-0.1814 = 0.5337.

A proportion of 0.5337 of the balances are between 600 and 1000, that is a 53.37%

I hope this helped you!

answer: i think it is (1,-2)

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is