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Mathematics

1 answer:

Afina-wow [57]3 years ago

3 0

Answer:

x=54°

Step-by-step explanation:

x+36°=90°

x=90°-36°

x=54°

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Suppose that the lifetime of tv tubes are normally distributed with a standard deviation of 1.1 years. Suppose that exactly 20%

IrinaK [193]

Answer:

4.924 years

Step-by-step explanation:

Lets denote X the lifetime of a tv tube (In years). X has distribution $N(\mu, 1.1)$ , with $\mu$ unknown.

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Lets call $Z = \frac{X - \mu}{1.1}$ the standarization of X. Z has distribution N(0,1), and its cummulative function, $\phi$ is tabulated. The values of $\phi$ can be found in the attached file.

$P(X < 4) = P(\frac{X - \mu}{1.1} < \frac{4 - \mu}{1.1}) = P(Z < \frac{4 - \mu}{1.1}) = \phi(\frac{4 - \mu}{1.1}) = 0.2$

The value q such that $\phi (q) = 0.2$ doesnt appear on the table. We can find it by using the symmetry of the normal density function. The opposite of q, -q must verify that $\phi(-q) = 0.8$ , hence -q must be equal to 0.84. Thus, q = -0.84