A student answered 86 problems on a test correctly and received a grade of 98%. How many problems were on the test, if all the p
1 answer:
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Answer: c. z = 1.35; Reject the null hypothesis
Step-by-step explanation:
Let be the average life expectancy of its batteries.
As per given , we have
Null hypothesis :
Alternative hypothesis :
Since is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.
Test statistic :
where, n= sample size
= sample mean
= Population mean
=population standard deviation
For , we have
Critical one-tailed test value for 0.10 significance level :
Decision : Since critical z value (1.28) < test statistic (1.35), so we reject the null hypothesis .
[When critical value is less than the test statistic value , we reject the null hypothesis .]
Answer:
Since the balls are drawn with replacement, it means the individual probability remain constant,
I have solved this problem on paper (Figures Attached).
Thanks.
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• 1 + cot² x = csc²x and csc x =
• sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Consider the left side
sin²Θ( 1 + cot²Θ )
= sin²Θ × csc²Θ
= sin²Θ × 1 / sin²Θ = 1 = right side ⇔ verified
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Consider the left side
cos²Θ - sin²Θ
= cos²Θ - (1 - cos²Θ)
= cos²Θ - 1 + cos²Θ
= 2cos²Θ - 1 = right side ⇒ verified