Simplify the expression plz
2 answers:
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Answer:
Option 2 50 ≤ s ≤ 100
Option 5 She could deposit $50
Option 6 She could deposit $75
Step-by-step explanation:
Let
s -----> amount of money Layla deposit into a saving account
we know that
25%=25/100=0.25
50%=50/100=0.50
so
----->
----->
The compound inequality is
<em>Verify each case</em>
case 1) 25 ≤ s ≤ 50
The statement is false
see the procedure
case 2) 50 ≤ s ≤ 100
<u>The statement is True</u>
see the procedure
case 3) s ≤ 25 or s ≥ 50
The statement is false
Because is s ≤ 100 and s ≥ 50
case 4) s ≤ 50 or s ≥ 100
The statement is false
Because is s ≤ 100 and s ≥ 50
case 5) She could deposit $50
<u>The statement is true</u>
Because the value of s satisfy the compound inequality
case 6) She could deposit $75
<u>The statement is true</u>
Because the value of s satisfy the compound inequality
Answer:
a) 68.26% probability that a student scores between 350 and 550
b) A score of 638(or higher).
c) The 60th percentile of test scores is 475.3.
d) The middle 30% of the test scores is between 411.5 and 488.5.
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:
a. What is the probability that a student scores between 350 and 550?
This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So
X = 550
has a pvalue of 0.8413
X = 350
has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
68.26% probability that a student scores between 350 and 550
b. If the upper 3% scholarship, what score must a student receive to get a scholarship?
100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88
A score of 638(or higher).
c. Find the 60th percentile of the test scores.
X when Z has a pvalue of 0.60. So it is X when Z = 0.253
The 60th percentile of test scores is 475.3.
d. Find the middle 30% of the test scores.
50 - (30/2) = 35th percentile
50 + (30/2) = 65th percentile.
35th percentile:
X when Z has a pvalue of 0.35. So X when Z = -0.385.
65th percentile:
X when Z has a pvalue of 0.35. So X when Z = 0.385.
The middle 30% of the test scores is between 411.5 and 488.5.