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PolarNik [594]
3 years ago
6

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 4 minutes and a stand

ard deviation of 3 minutes.
Sixty percent of the time, it takes more than how many minutes to find a parking space?
Mathematics
1 answer:
DedPeter [7]3 years ago
6 0

Answer:

3.24 minutes

Step-by-step explanation:

Use a calculator or chart to find the z-score.

P(Z > z) = 0.60

P(Z < z) = 0.40

z = -0.253

Find the time associated with the z-score.

z = (x − μ) / σ

-0.253 = (x − 4) / 3

x = 3.24

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A report by the US Geological Survey indicates that glaciers in Glacier National Park, Montana, are shrinking. Recent estimates
postnew [5]

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a) C

b) B

c) C, E

d) 15.5

e) 0.7

f) 67.7

Step-by-step explanation

a) A linear equation can be written as y=mx+c where m is the slope and c is the intercept on the y-axis. The slope describes how y changes when x changes. A negative value means the it is a decreasing change. In our case, y is A and x is t. Thus, the slope of the equation is m=-0.062. This means that the area of glacier is decreasing by 0.062 \text{km}{}^2 = 62000 \text{m}{}^2 every year since 2000.

b) The A-intercept (= 16.2 \text{km}{}^2) represents the area covered when t=0. But t=0 starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2 \text{km}{}^2.

c) A=f(t) means the area covered after year 2000. Setting it to 12 means the area covered after t years is 12 \text{km}{}^2). t is therefore the number of years since 2000 that the total area covered will be 12 \text{km}{}^2).

d) f(12)=16.2−0.062\times12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2 to 1 decimal place.

e) The term involving t represents the disappearing area. In 12 years, the disappeared area is 0.062\times12=0.744 =0.7 \text{km}{}^2 to 1 decimal place.

f) f(t)=16.2−0.062t =12

0.062t = 16.2-12 = 4.2

t = \dfrac{4.2}{0.062}=67.7419\ldots =67.7 years to 1 decimal place.

8 0
3 years ago
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