Megan hughes deposits $4300 in an account that pays simple interest. when she withdraws her money 7 months later, she receives
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The very first thing to do in every correlation activity is to plot the gathered data points in a scatter plot. It is better to use software tools like MS Excel because they have a feature there that uses linear regression like that one shown in the picture.
Once you plot the data points, make a trendline. You are given with options. If you want a linear function, then you will have a linear model with a function equation of y = 0.2907x + 2.2643. It has a correlation coefficient of 0.9595. That's a strong correlation already. The R² value tells how good your model fits the data points. If you want to increase the R², a better model would be a quadratic function with the equation, y = -0.0209x²+0.506x+2.0232. As you can see the R² increase even more to 0.9992.
Once you plot the data points, make a trendline. You are given with options. If you want a linear function, then you will have a linear model with a function equation of y = 0.2907x + 2.2643. It has a correlation coefficient of 0.9595. That's a strong correlation already. The R² value tells how good your model fits the data points. If you want to increase the R², a better model would be a quadratic function with the equation, y = -0.0209x²+0.506x+2.0232. As you can see the R² increase even more to 0.9992.
Answer:
71.08% probability that pˆ takes a value between 0.17 and 0.23.
Step-by-step explanation:
We use the binomial approxiation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
. So
In other words, find probability that pˆ takes a value between 0.17 and 0.23.
This probability is the pvalue of Z when X = 200*0.23 = 46 subtracted by the pvalue of Z when X = 200*0.17 = 34. So
X = 46
has a pvalue of 0.8554
X = 34
has a pvalue of 0.1446
0.8554 - 0.1446 = 0.7108
71.08% probability that pˆ takes a value between 0.17 and 0.23.