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Helen [10]
3 years ago
14

The comprehensive strength of concrete is normally distributed with μ = 2500 psi and σ = 50 psi. Find the probability that a ran

dom sample of n = 5 specimens will have a sample mean diameter that falls in the interval from 2499 psi to 2510 psi.
Mathematics
1 answer:
VARVARA [1.3K]3 years ago
8 0

Answer:

The probability that the diameter falls in the interval from 2499 psi to 2510 psi is 0.00798.

Step-by-step explanation:

Let's define the random variable, X = "Comprehensive strength of concrete". We have information that X is normally distributed with a mean of 2500 psi and a standard deviation of  50 psi (or a variance of 2500 psi). In other words, X \sim N(2500, 2500).

We want to know the probability of the mean of X or \bar{X} that falls in the interval [2499;2510]. From inference theory we know that :

\bar{X} \sim N(2500, \frac{2500}{5}) \Rightarrow \bar{X} \sim N(2500,500)

Now we can find the probability as follows:

P(2499 \leq \bar{X} \leq 2510) \Rightarrow P(\frac{2499 - 2500}{500} \leq \frac{\bar{X} - 2500}{500} \leq \frac{2499 - 2500}{500} ) \Rightarrow\\\Rightarrow P(-0.002 \leq \frac{\bar{X} - 2500}{500} \leq 0.02 ) \Rightarrow P(-0.002 \leq Z \leq 0.02 )

Where Z \sim N(0,1), then:

P(-0.002 \leq Z \leq 0.02 ) \approx P(0 \leq Z \leq 0.02 ) = P(Z \leq 0.02 ) - P(Z \leq 0) \\P(0 \leq Z \leq 0.02 ) = 0.50798 - 0.5 = 0.00798

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Step-by-step explanation:

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3 years ago
A red balloon starts at 7.3 meters off the ground and rises at 2.6 meters per second. A blue balloon starts at 12.4 meters off t
nexus9112 [7]
This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both the red balloon and the blue balloon. 

Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s: 

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Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:

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Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation: 

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Last, we divide both sides by 1.1. So s = 4.63. 

This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation: 

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After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.
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