Answer:
0.91517
Step-by-step explanation:
Given that SAT scores (out of 1600) are distributed normally with a mean of 1100 and a standard deviation of 200. Suppose a school council awards a certificate of excellence to all students who score at least 1350 on the SAT, and suppose we pick one of the recognized students at random.
Let A - the event passing in SAT with atleast 1500
B - getting award i.e getting atleast 1350
Required probability = P(B/A)
= P(X>1500)/P(X>1350)
X is N (1100, 200)
Corresponding Z score = 

Distribute
y+10+c=z
minus y from both sides
10+c=z-y
minus 10 both sides
c=z-y-10
Answer:
47.06% of the population has an IQ between 85 and 105.
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:

What percent of the population has an IQ between 85 and 105?
This is the pvalue of Z when X = 105 subtracted by the pvalue of Z when X = 85. So
X = 105



has a pvalue of 0.6293.
X = 85



has a pvalue of 0.1587
So 0.6293 - 0.1587 = 0.4706 = 47.06% of the population has an IQ between 85 and 105.
199175$ 128,500 x 0.55 = 70,675. 128,500+70,675= 199,175
Answer:
The minimum unit cost is equal to $15,339
Step-by-step explanation:
Let
x ----> the number of engines
C ---> the cost in dollars to make each airplane engine
we have

This is a vertical parabola open upward (the leading coefficient is positive)
The vertex represent the minimum of the parabola
The minimum unit cost is equal to the y-coordinate of the vertex
Convert the quadratic equation into vertex form
Factor 0.5

Complete the square. Remember to balance the equation by adding the same constants to each side


Rewrite as perfect squares
----> equation into vertex form
The vertex is the point (100,15,339)
The y-coordinate of the vertex is 15,339
therefore
The minimum unit cost is equal to $15,339