The resistance of a certain type of electrical resistors has normal distribution with mean of 45 ohms. A random sample of 9 such resistors is selected, and the variance is computed to be 4. What is the probability that the average resistance will exceed 47 ohms?

0.00135

Step-by-step explanation:

When given a random sample of numbers:

z-score is is z = (x-μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation.

Standard deviation = √variance = √4 = 2

Mean = 45 ohms

A random sample of 9 such resistors

z = 47 - 45/2 / √9

z = 2/2/3

z = 3

P-value from Z-Table:

P(x<47) = 0.99865

P(x>47) = 1 - P(x<47) = 0.0013499

Approximately ≈ 0.00135

The probability that the average resistance will exceed 47 ohms is 0.00135

The answer is
LA to Page: 611 mi
Page to Denver: 406 mi

Total distance from LA to Denver is T.
The distance LA to Page is x
The distance Page to Denver is y.

T = x + y
T = 1017

x + y = 1017

The distance from L.A. to Page (x) is 205 miles greater than the distance from Page to Denver (y):
x = y + 205

The system of two equations:
x + y = 1017
x = y + 205

Substitute x from the second equation into the first one:
y + 205 + y = 1017
2y + 205 = 1017
2y = 1017 - 205
2y = 812
y = 812 / 2
y = 406 mi (Page to Denver)

x = y + 205 = 406 + 205 = 611 mi (LA to Page)