Please help, I’ll mark your answer as brainliest.
1 answer:
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Answer:
x = 72
Step-by-step explanation:
<u>To solve for 'x', isolate it</u>. This means to keep 'x' on one side of the equal sign, while moving the other numbers to the other side. The numbers on the other side will tell you what 'x' equals to.
<u>When 'moving' a number to the other side, you cancel it out where it originally is by doing reverse operations</u>. (Reverse operation pairs are addition/subtraction and division/multiplication). To keep an equation balanced, <u>what you do to one side you have to do to the other</u>.
Keep 'x' on the left and move everything over.
Add 17 to both sides. "-17" cancels out on the left.
Simplified right side
Because 3/8 originally multiplies with 'x', do the reverse: divide both sides by 3/8.
To divide a fraction, change to multiplication and flip the fraction's top and bottom numbers.
Combine the factors into one fraction.
Multiply 27 by 8 in the numerator.
Simplify the fraction by dividing top by bottom.
Final answer, solved for 'x'
Answer:
1) Randomization: We assume that we have a random sample of students
2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size
3) np = 500*0.66= 330 >10
n(1-p) = 500*(1-0.66) =170>10
So then we can use the normal approximation for the distribution of p, since the conditions are satisfied
The population proportion have the following distribution :
And we have :
Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).
Step-by-step explanation:
For this case we know that we have a sample of n = 500 students and we have a percentage of expected return for their sophomore years given 66% and on fraction would be 0.66 and we are interested on the distribution for the population proportion p.
We want to know if we can apply the normal approximation, so we need to check 3 conditions:
1) Randomization: We assume that we have a random sample of students
2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size
3) np = 500*0.66= 330 >10
n(1-p) = 500*(1-0.66) =170>10
So then we can use the normal approximation for the distribution of p, since the conditions are satisfied
The population proportion have the following distribution :
And we have :
And we can use the empirical rule to describe the distribution of percentages.
The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
• The probability of obtain values within one deviation from the mean is 0.68
• The probability of obtain values within two deviation's from the mean is 0.95
• The probability of obtain values within three deviation's from the mean is 0.997
Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).