The train station clock runs too fast and gains 7 minutes every 4 days. How many minutes and seconds will it have gained at the
1 answer:
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Answer:
1) 22.66%
2) 20
Step-by-step explanation:
The scores of a test are normally distributed.
Mean of the test scores = u = 22
Standard Deviation = = 4
Part 1) Proportion of students who scored atleast 25 points
Since, the test scores are normally distributed we can use z scores to find this proportion.
We need to find proportion of students with atleast 25 scores. In other words we can write, we have to find:
P(X ≥ 25)
We can convert this value to z score and use z table to find the required proportion.
The formula to calculate the z score is:
Using the values, we get:
So,
P(X ≥ 25) is equivalent to P(z ≥ 0.75)
Using the z table we can find the probability of z score being greater than or equal to 0.75, which comes out to be 0.2266
Since,
P(X ≥ 25) = P(z ≥ 0.75), we can conclude:
The proportion of students with atleast 25 points on the test is 0.2266 or 22.66%
Part 2) 31st percentile of the test scores
31st percentile means 31%(0.31) of the students have scores less than this value.
This question can also be done using z score. We can find the z score representing the 31st percentile for a normal distribution and then convert that z score to equivalent test score.
Using the z table, the z score for 31st percentile comes out to be:
z = -0.496
Now, we have the z scores, we can use this in the formula to calculate the value of x, the equivalent points on the test scores.
Using the values, we get:
Thus, a test score of 20 represent the 31st percentile of the distribution.
A. (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work and provide your answer in scientific notation. Jupiter = 778,500,000 km from sun. Venus = 108,200,000 km from sun.
778,500,000 – 108,200,000 = 670,300,000
It would need to travel 670,300,000 km/ 6.703 x 10 with a 8 squared km (as shown below)
B.Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer. Mercury = 57,909,000 km Venus = 108,200,000 km Earth = 149,600,000 km 57,909,000 + 108,200,000 + 149,600,000 = 315,709,000 Less because 315,709,000 km is less than 4,498,000,000 km
C.If Earth was 10 times farther away from the sun than it is now, which planet would it be closest to? (Assume all the planets are aligned with the sun and are on the same side of the sun.) Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work. Earth = 149,600,000 km 149,600,000 x 10 = 1,496,000,000 Earth’s new distance = 1,496,000,000 Earth would be closest to Saturn. 1,496,000,000 – 1,429,000,000 = 67,000,000
They would be 67,000,000 km apart
Scientific notation: 6.7 x 10 with a 7 squared km (sorry I can't write this to show this figure but see below as you should write it exactly like how I typed it below followed by km)
D. The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work. Convert your answer into scientific notation if necessary. Earth = 149,600,000 km
Saturn = 1,429,000,000 km
1,429,000,000 - 149,600,000 = 1,279,400,000
1,279,400,000 km
1,279,400,000 ÷ 28,000 = 45,692.8
Estimated hours it will take the shuttle to reach Saturn from Earth = 45,693
Scientific notation: 4.5693 x 10 with a 4 squared
(same with this one, it should be written as I have it shown below instead of how I first tried to explain it.)
778,500,000 – 108,200,000 = 670,300,000
It would need to travel 670,300,000 km/ 6.703 x 10 with a 8 squared km (as shown below)
B.Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer. Mercury = 57,909,000 km Venus = 108,200,000 km Earth = 149,600,000 km 57,909,000 + 108,200,000 + 149,600,000 = 315,709,000 Less because 315,709,000 km is less than 4,498,000,000 km
C.If Earth was 10 times farther away from the sun than it is now, which planet would it be closest to? (Assume all the planets are aligned with the sun and are on the same side of the sun.) Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work. Earth = 149,600,000 km 149,600,000 x 10 = 1,496,000,000 Earth’s new distance = 1,496,000,000 Earth would be closest to Saturn. 1,496,000,000 – 1,429,000,000 = 67,000,000
They would be 67,000,000 km apart
Scientific notation: 6.7 x 10 with a 7 squared km (sorry I can't write this to show this figure but see below as you should write it exactly like how I typed it below followed by km)
D. The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work. Convert your answer into scientific notation if necessary. Earth = 149,600,000 km
Saturn = 1,429,000,000 km
1,429,000,000 - 149,600,000 = 1,279,400,000
1,279,400,000 km
1,279,400,000 ÷ 28,000 = 45,692.8
Estimated hours it will take the shuttle to reach Saturn from Earth = 45,693
Scientific notation: 4.5693 x 10 with a 4 squared
(same with this one, it should be written as I have it shown below instead of how I first tried to explain it.)