Sketch a normal distribution with µ = 80 and σ = 10. What is the probability of randomly selecting a score greater than 100 from
this distribution?
1 answer:
Answer:
The sketch is provided in attached file.
0.0228
Step-by-step explanation:
The sketch is made by taking center at µ=80 and the desired probability of the mentioned area is also demonstrates.
The probability randomly selecting a score greater than 100 from this distribution can be calculated as
P(X>100)=P((X-µ)/σ > (100-80)/10)
P(X>100)=P(z>2)
P(X>100)=P(0<z<∞)-P(0<z<2)
Using normal table the probability corresponds to z-score=2 is 0.0228 and the area on the right side of normal curve is 0.5. So,
P(X>100)=0.5-0.4772=0.0228
The probability randomly selecting a score greater than 100 is 2.28%.
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Answer:
a. 1 1/8 b. 8/9
Step-by-step explanation:
You can set this up as a proportion to solve. For part a. we know that 2/3 of the road is 3/4 mile long. 2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length. Set up the proportion like this:
Cross multiplying gives you:
The 3's on the right cancel out nicely, leaving you with
To solve for x, multiply both sides by 3/2:
gives you
That means that the road is still missing 3/8 of a mile til it's finished. The length of the road is found by adding the 3/4 to the 3/8:
So the road is a total of 1 1/8 miles long.
For b. we need to find out how much of 1 1/8 is 1 mile:
1 mile = x * 9/8 and
x = 8/9. When 1 mile of the road is completed, that is 8/9 of the total length of the road completed.