The length of a standard IMAX screen is 34 feet less than twice it’s width. The perimeter of the screen is 250 feet. What are th
1 answer:
You might be interested in
Answer:
use f(x)=y=mx+b
let snow = S, time = t instead of y and x
S(t)=mt+b
The rate of inches per hour represents the slope of the graph, m.
The y-variable would be the amount of snow, S.
The x-variable would be the time, t, in hours.
The function has three pieces:
i) S(t)= 2t (slope = 2)
ii) S(t) = 3t (slope = 3)
iii) S(t) = 0.75t (slope = 0.75)
For the first piece, i), t=3, so the amount of snow is 6 inches.
For the second piece, ii) t=5, so the amount of snow is 15 inches.
For the third piece, iii) t=1, so the amount of snow is 0.75 inch.
In total, it snowed 21.75 inches.
total snow
Answer:
a) 33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.
b) 0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are 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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
a) What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?
This is 1 subtracted by the pvalue of Z when X = 21. So
has a pvalue of 0.67
1 - 0.67 = 0.33
33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.
b) The average score of the 76 students at Northside High who took the test was x =20.4. What is the probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher?
Now we have
This probability is 1 subtracted by the pvalue of Z when X = 20.4. So
By the Central Limit Theorem
has a pvalue of 0.9961
1 - 0.9961 = 0.0039
0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher