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Calculating probability under a standard normal curve

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We are estimating the spares requirement for a radar power supply. The power supply was designed with a mean (μ) life of 6500 hours. The standard deviation (σ) determined from testing is 750 hours. What is the likelihood that a power supply would fail in less than 4880 hours?

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The solution gives detailed steps on calculating the likelihood that a power supply would fail in less than 4880 hours under a standard normal curve.

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Calculating the probabilities under a standard normal curve

The time spent using e-mail per session is normally distributed, µ = 8 minutes and σ = 2 minutes. If you select a random sample of 25 sessions, then:

a. What is the probability that the sample mean is between 7.8 and 8.2 minutes?
b. What is the probability that the sample mean is between 7.5 and 8.2 minutes?
c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 7.8 and 8.2 minutes?
d. Explain the difference in the results of (a) and (c)

2.
The amount of time a bank teller spends with each customer has a population mean,µ, of 3.10 minutes and standard deviation, σ , of 0.40 minute. If you select a random sample of 16 customers,
a) What is the probability that the mean time spent per customer is at least 3 minutes?
b) There is an 85 % chance that the sample mean is less than how many minutes?
c) What assumption must you make in order to solve a) and b)?
d) If you select a random sample of 64 customers, there is an 85% chance that the sample mean is less than how many minutes?

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