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malfutka [58]
3 years ago
8

Suppose the sediment density (g/cm3 ) of a randomly selected specimen from a certain region is known to have a mean of 2.80 and

standard deviation of 0.85. If a random sample of 35 specimens is selected, what is the probability that the sample average sediment density is at most 3.00?
Mathematics
1 answer:
Irina18 [472]3 years ago
4 0

Answer:

0.918 is the probability that the sample average sediment density is at most 3.00

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 2.80

Standard Deviation, σ = 0.85

Sample size,n = 35

We are given that the distribution of sediment density is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

Standard error due to sampling:

=\dfrac{\sigma}{\sqrt{n}} = \dfrac{0.85}{\sqrt{35}} = 0.1437

P(sample average sediment density is at most 3.00)

P( x \leq 3.00) = P( z \leq \displaystyle\frac{3.00 - 2.80}{0.1437}) = P(z \leq 1.3917)

Calculation the value from standard normal z table, we have,  

P(x \leq 3.00) = 0.918

0.918 is the probability that the sample average sediment density is at most 3.00

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