Respuesta :
Answer:
Probability that their mean credit card balance is less than $2500 is 0.0073.
Step-by-step explanation:
We are given that a bank auditor claims that credit card balances are normally distributed, with a mean of $3570 and a standard deviation of $980.
You randomly select 5 credit card holders.
Let [tex]\bar X[/tex] = sample mean credit card balance
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean credit card balance = $3570
[tex]\sigma[/tex] = standard deviation = $980
n = sample of credit card holders = 5
Now, the probability that their mean credit card balance is less than $2500 is given by = P([tex]\bar X[/tex] < $2500)
P([tex]\bar X[/tex] < $2500) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{2500-3570}{\frac{980}{\sqrt{5} } }[/tex] ) = P(Z < -2.44) = 1 - P(Z [tex]\leq[/tex] 2.44)
= 1 - 0.9927 = 0.0073
The above probability is calculated by looking at the value of x = 2.44 in the z table which has an area of 0.9927.
Therefore, probability that their mean credit card balance is less than $2500 is 0.0073.
