Yoshi is painting a large wall in the park. He measures the wall and finds that the dimensions are 4 m by 20 m. Yoshi has a can
1 answer:
You might be interested in
In calculus, we use derivatives to find the instantaneous rate of change at any point on a graph. To find the average rate of change, we just find the slope of the secant line that intercepts two points on the graph.
We find slope with the following equation:
In this case, we are looking for the slope from x = -1 to x = 1. We have both x values, so next we need the y values.
F(-1) = (-1)^2 - (-1) - 1 = 1
F(1) = (1)^2 - (1) - 1 = -1
Now plug in the x and y values to find the slope:
The answer is -1.
We find slope with the following equation:
In this case, we are looking for the slope from x = -1 to x = 1. We have both x values, so next we need the y values.
F(-1) = (-1)^2 - (-1) - 1 = 1
F(1) = (1)^2 - (1) - 1 = -1
Now plug in the x and y values to find the slope:
The answer is -1.
Answer:
a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b) The weight that 80% of the apples exceed is of 78.28g.
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.
Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.
This means that
a. Find the probability a randomly chosen apple exceeds 100 g in weight.
This is 1 subtracted by the p-value of Z when X = 100. So
has a p-value of 0.9697
1 - 0.9696 = 0.0304
0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.
b. What weight do 80% of the apples exceed?
This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.
The weight that 80% of the apples exceed is of 78.28g.