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Chips suppose a computer chip manufacturer rejects 2% of the chips produced because they fail presale testing.

Artyom0805 [142]

(a) P( fifth one is bad) = P( first 4 are OK) * P(5th is bad)

= (0.98)^4 * 0.02 = 0.0184 or 1.84%

(b) this will be (0.98)^10 = 81.70%

4 0

3 years ago

g Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distrib

algol13

Answer:

The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .