Answer:
182.41
Step-by-step explanation:
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.
In this problem, we have that:
40th percentile
Value of X when Z has a pvalue of 0.4. So X when Z = -0.253.
So the answer is 182.41.
Answer: A. 5%
Step-by-step explanation:
Given : The chance that they will join the graduate program : p=0.10
The total number of students in the class: n = 400
For this binomial situation :
We assume that this is normal distribution.
Let X be the random variable that represents the students will be joining a graduate program.
Z-score : 
For x= 50 , we have
Using the standard normal distribution table , we have
Hence, the value i.e.closest to the probability that at least 50 students will be joining a graduate program = 5%
9514 1404 393
Answer:
see below for the graph
Step-by-step explanation:
We can specify the location of the minimum and the axis of symmetry using the vertex form of the quadratic equation:
y = a(x -h)² +k . . . . . . . vertex (h, k); scale factor 'a'
We can put the given values into the equation to see what 'a' needs to be to make the function have the desired y-intercept.
-3 = a(0 -(-2))² +(-5)
2 = 4a . . . . add 5 and simplify
a = 1/2 . . . . divide by 4
The equation for the desired function can be ...
y = 1/2(x +2)² -5
This function is in the form y=mx + b where m is your slope, so the slope is -2
