There are 2.54 centimeters in an inch how many inches are in 51.78 centimeters round to the nearest tenths

1 answer:

3 0

2.54 cm in 1 inch......how many inches in 51.78 cm...

51.78 / 2.54 = 20.4 inches <==

or this way...
2.54 / 1 = 51.78 / x....2.54 cm to 1 in = 51.78 cm to x inches
cross multiply
(2.54)(x) = 51.78)(1)
2.54x = 51.78
x = 51.78 / 2.54
x = 20.4 inches <==

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

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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:

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