Answer:
The probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.9375
Step-by-step explanation:
Let E be a random variable denoting the event that an artist makes a craft item with satisfactory level.
Then the random variable E follows a Geometric distribution.
A Geometric distribution is defined as the number of failures (<em>k</em>) before the first success.
The probability function of Geometric distribution is:
, <em>p</em> = Probability of success and <em>k</em> = 0, 1, 2, 3...
The probability of success is, <em>p</em> = 0.5 and the number of failures is, <em>k</em> = 3.
Compute the probability of at most 3 attempts before the first success is:
Therefore, the probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.9375.
Answer:
y = 32
Step-by-step explanation:
Given y is directly proportional to x² then the equation relating them is
y = kx² ← k is the constant of proportion
To find k use the condition when x = 3, y = 4.5 , then
4.5 = k × 3² = 9k ( divide both sides by 9 )
0.5 = k
y = 0.5x² ← equation of proportion
When x = 8 , then
y = 0.5 × 8² = 0.5 × 64 = 32
Answer:
Alternative hypothesis:
Step-by-step explanation:
Given that:
Sample 1:
Sample size = 10
Sample mean = 79.3
Standard deviation = 22.4
Sample 2:
Sample size = 10
Sample mean = 82.1
Standard deviation = 12.0
To find the alternative hypothesis.
The null and alternative hypothesis can be computed as follows:
Null hypothesis:
Alternative hypothesis:
Since, alternative hypothesis is ≠, it shows that it is a two tailed test.
You posted a lot of questions. I'll do the first four problems to get you started.
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Problem 1
This sequence is arithmetic because we add the same amount (4) each time to get the next term. The first term is -2. The first five terms are: -2, 2, 6, 10, 14
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Problem 2
This sequence is geometric. We multiply each term by 1/4 to get the next term. We start with 8 as the first term. The first five terms are 8, 2, 1/2, 1/8, 1/32.
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Problem 3
Similar to problem 1. This time we're adding -19 to each term to get the next one. The starting term is -6. This sequence is arithmetic and the first five terms are -6, -25, -44, -63, -82
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Problem 4
Similar to problem 2. This sequence is geometric with common ratio 2/3. First term is 6. The first five terms are 6, 4, 8/3, 16/9, 32/27
Answer:
0.1034 = 10.34% probability that the first student selected is an accounting major and the second student is a history major
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
14 account majors from a set of 29 students.
Then, 6 history majors from a set of 29 - 1 = 28 students.
So
0.1034 = 10.34% probability that the first student selected is an accounting major and the second student is a history major