What is the relationship between 0.04 and 0.004?

Final answer:

To find the value of z such that 0.11 of the area lies to the right of z, use the standard normal probability table. The value of z is approximately 1.96.

Explanation:

To find the value of z such that 0.11 of the area lies to the right of z, we can use the standard normal probability table. The area to the right of z is equal to 1 minus the area to the left of z.

Using the information given, the area to the left of z that corresponds to a value of 0.025 is 0.975. The area to the left of 1.96, which can be found using the standard normal probability table, is 0.975.

Therefore, the value of z is approximately 1.96.

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Answer:

1.23?

Step-by-step explanation:

Answer:

m= -90 is your answer

Step-by-step explanation:

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a. The probability that at least 13 of the next 15 motherboards pass inspection is 0.604.

b. On average, 1.1765 motherboards should be inspected until a motherboard that passes inspection is found.

a.

The formula for the probability of getting exactly k successes in n trials with a success probability of p is:

Where "n choose k" represents the binomial coefficient, which is calculated as n! / (k! * (n - k)!), where "!" denotes factorial.

In this case:

n = 15 (number of trials)

k = 13, 14, 15 (number of successes)

p = 0.85 (probability of success)

First, let's calculate the probability that exactly 13, 14, and 15 motherboards pass inspection.

For k = 13:

= 0.28564

For k = 14:

= 0.23123

For k = 15:

= 0.08735

Now, sum these probabilities to get the final answer:

P(at least 13) = P(X = 13) + P(X = 14) + P(X = 15)

= 0.28564 + 0.23123 + 0.08735

= 0.60422

= 0.604

(b)

The average number of trials needed until a motherboard that passes inspection is found can be calculated using the concept of the expected value of a geometric distribution:

Expected value (E) = 1 / p

Where p is the probability of success.

In this case, p = 0.85.

E = 1 / 0.85

= 1.1765

Thus, on average, 1.1765 motherboards should be inspected until a motherboard that passes inspection is found.

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Final answer:

To find the probability that at least 13 of the next 15 motherboards pass the inspection, use the binomial formula for each scenario (13, 14, and 15 passing) and sum the results. To find on average how many motherboards need to be inspected for one to pass inspection, just take the reciprocal of the probability of success (1/0.85).

Explanation:

This question falls under the domain of probability and statistics. Let's tackle each part separately:

(a) When we talk about at least 13 out of 15 motherboards passing, we have to consider the situations where exactly 13, 14, or all 15 pass. For each case, you would use the binomial formula P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)). In this formula, n is the number of trials (which is 15), k is the number of successes we are interested in, p is the probability of a success (which is 0.85), C(n, k) is a combination that represents the different ways k successes can happen in n trials. Calculate this for k = 13, 14, and 15 and sum the results to get the probability for at least 13 to pass.

(b) To find on average how many motherboards should be inspected until one passes is straightforward - it is simply the reciprocal of the probability of success which is 1/0.85.

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Answer: 17.5

Step-by-step explanation: