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zhannawk [14.2K]
3 years ago
11

HELP TIMED! WILL MARK BRAINLIEST Nolan began a savings account three years ago. He invested $100 at a 2% interest rate according

to the equation Vn = 100(1.02)x, where Vn is the value of his account after x years. Anias started an account today. She invested $100 at a 2% interest rate according to the equation Va = 100(1.02)x–3, where Va is the value of her account. Let’s say Anias started saving at the same time Nolan did, three years ago. Approximately how much money would she have had to invest to have the same amount of money she has now?

Mathematics
1 answer:
MAVERICK [17]3 years ago
6 0
I believe it’s c.... I’m sorry if it’s wrong
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Answer:

They should guarantee the lifetime of their batteries for 32 months.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 36 months and a standard deviation of 2 months.

This means that \mu = 36, \sigma = 2

If the company wants to replace no more than 2% of all batteries, for how many months should they guarantee the lifetime of their batteries?

The guarantee should be the 2th percentile of lengths, which is X when Z has a pvalue of 0.02. So X when Z = -2.054.

Z = \frac{X - \mu}{\sigma}

-2.054 = \frac{X - 36}{2}

X - 36 = -2.054*2

X = 31.89

Rounding to the closest month, 32.

They should guarantee the lifetime of their batteries for 32 months.

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