a customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. the total bill was $94.75. write and solv
2 answers:
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Answer:
d. 0.303
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
In this question:
We want the probability of Sean having a greater income than Evan, which is the probability of the subtraction of Sean's income by Evan's income is greater than 0.
Distribution of the difference between Sean's and Evan's income:
Sean has mean 225, Evan 240. So
Sean's standard deviation is of 25, Evan's of 15. So
Probability that Sean will have a greater income than Evan in a randomly selected week:
Probability of the subtraction being greater than 0, which is 1 subtracted by the pvalue of Z when X = 0. So
has a pvalue of 0.695
1 - 0.695 = 0.305.
Closest to 0.303, option d.
To find the value f(-7), we just need to evaluate the function at 
. In other words, we are going to replace 
with -7 in the function:
Similarly, to find the value of f(5), we just need to evaluate the function at
. In other words, we are going to replace with 5 in the function:
We can conclude that and
Similarly, to find the value of f(5), we just need to evaluate the function at
We can conclude that