Math 116 Essay
Provide an appropriate response. 1)
Two random variables are normally distributed with the same mean. One has a standard deviation of 10 while the other has a standard deviation of 15. How will the graphs of the two variables differ and how will they be alike? 2)
Which is larger, the area under the standard normal curve between 1 and 1, or the area under the standard normal curve between 0 and 2? Explain your reasoning. 3)
Which of the variables below do you think will be roughly normally distributed?
a. Weights of 10 year old boys
b. Incomes of 40 year old adults
c. The numbers that show up when you roll a balanced die
d. The amount of coffee …show more content…
The probability of more than 49 correct answers 19)
The probability of fewer than 48 democrats
For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. 20) n = 27 and p = 0.6 21) n = 19 and p = 0.8
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. 22)
Estimate the probability of getting exactly 43 boys in 90 births. 23)
A certain question on a test is answered correctly by 22% of the respondents. Estimate the probability that among the next 150 responses there will be at most 40 correct answers.
Provide an appropriate response. 24)
Fill in the blanks.
A fair coin is flipped 280 times. You wish to find the probability that the number of tails is greater than 160. This probability can be estimated by finding the area to the right of _____ under the normal curve with μ = ____ and σ = ___.
1)
Both graphs will have the same shape (they will both be bellshaped) and they will be centered at the same place (the common mean). The graph of the variable with the smaller standard deviation will be narrower and taller than the other graph.

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