Given the following process control data for a normally distributed quality variable (four samples of size five each): Sample Measurements
8am 11.6 11.9 12.0 12.2 11.8
9am 12.1 11.8 11.9 12.0 11.8
10am 11.8 12.9 12.1 12.8 11.9
11am 12.0 12.2 12.1 12.2 13.0

If the process is known to have a mean of 12.0 and an average range of 0.5 (5 observations per sample), using three-sigma control limits, do any of the sample means indicate an out-of-control process, and if so, which specifically?

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of the three mortgage options that demarco and tanya have to choose from, the balloon payment mortgage would be their best option, over adjustable payment and fixed payment plans.ultimately, the balloon payment plan would save demarco and tanya overall, in interest, would cost less monthly, and they would only have to make these payments for 8 years, opposing to 30 years for adjustable or fixed payment plans. 

overall, demarco and tanya would save $80,811 if they chose balloon payments over fixed payments, and would save $116,711 if they choose balloon payments over adjustable payments. benefits with choosing fixed payments over adjustable payments is that, in the end, the payments will still be $836.30 a month, while with adjustable payments, the initial monthly payments will be $763.38 to $1082.70 a month, ultimately leading to a more costly purchase. benefits with choosing fixed payments over balloon payments are not present. benefits in choosing adjustable payments over is that it has a lower interest rate, and starts with lower monthly payments initially. benefits in choosing adjustable payments over balloon payments include a lower interest rate, and lower initial monthly payments. benefits in choosing balloon payments over fixed payments include lower interest rates, lower overall price, lower monthly payments, takes less time to pay off, and does not require a downpayment. benefits in choosing balloon payments over adjustable payments include, lower monthly payments (when averaged), takes less time to pay off, and lower overall price.

hence, option c, balloon payments, is the best option for demarco and tanya to make this purchase, for it will save them a minimum of $80811, and a maximum of $116,711.