mr and mrs gracia took their three children to see a matinee on saturday. they spent a total of 55.50, which included 29.95 at t
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Answer:
(a) The proportion of tenth graders reading at or below the eighth grade level is 0.1673.
(b) The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.198, 0.260).
Step-by-step explanation:
Let <em>X</em> = number of students who read above the eighth grade level.
(a)
A sample of <em>n</em> = 269 students are selected. Of these 269 students, <em>X</em> = 224 students who can read above the eighth grade level.
Compute the proportion of students who can read above the eighth grade level as follows:
The proportion of students who can read above the eighth grade level is 0.8327.
Compute the proportion of tenth graders reading at or below the eighth grade level as follows:
Thus, the proportion of tenth graders reading at or below the eighth grade level is 0.1673.
(b)
the information provided is:
<em>n</em> = 709
<em>X</em> = 546
Compute the sample proportion of tenth graders reading at or below the eighth grade level as follows:
The critical value of <em>z</em> for 95% confidence interval is:
Compute the 95% confidence interval for the population proportion as follows:
Thus, the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.198, 0.260).
Answer:
see the explanation
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
m∠PQS+m∠SQR=m∠PQR ----> equation A (by Addition Angle Postulate)
we have that
m∠PQR=90° ----> equation B given problem (because is a right angle)
substitute equation B in equation A
m∠PQS+m∠SQR=90°
Remember that
Two angles re complementary is their sum is equal to 90 degrees (Definition of complementary angles)
therefore
m∠PQS and m∠SQR are complementary angles
