F(-3) means x = -3

Look at the functions above, if x <= - 3 then use F(x) = 7 - x

so
F(-3) = 7 - x, replace x = - 3 into the function
F(-3) = 7 - (-3)
F(-3) = 7 + 3
F(-3) = 10

7 0

3 years ago

The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution

ankoles [38]

Answer:

a) Normal Distribution

b) 0.146

c) 0.070

Step-by-step explanation:

We are given the following information in the question:

The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4

a) $\bar{x}$ : mean number of accidents per week at the intersection during a year (52 weeks)

According to central limit theorem, as the sample size becomes larger, the distribution of mean approaches a normal distribution.

Since we have a large sample, the approximate distribution of $\bar{x}$ is a normal distribution with

$\text{Mean} = 2.2\\\text{Standard Deviation} = \displaystyle\frac{\sigma}{\sqrt{n}} = \frac{1.4}{\sqrt{52}} = 0.19$

b) P(mean is less than 2)

Formula:

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

P(x > 610)

$P( \bar{x} < 2) = P( z < \displaystyle\frac{2 - 2.2}{0.19}) = P(z < -1.052)$

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

$P(\bar{x} < 2) = 0.146$

c) P(fewer than 100 accidents at the intersection in a year)

P(x < 100)

$P( \bar{x} < \frac{100}{52}) =P(\bar{x} < 1.92) =P(z < \displaystyle\frac{1.92 - 2.2}{0.19}) = P(z < -1.473)$

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

$P(x$

7 0

3 years ago

Write in standard form<br> y-3x=1

kvasek [131]

The standard form is y=mx+b.
With y-3x=1, you're trying to get y by itself.
Start with adding 3x to both sides to get y=3x+1

5 0

4 years ago