is it appropriate to use the normal distribution to approximate the sampling distribution of $ \hat{p} $ for the following?$ n = 350, p = 0.99 $$ \circ $ no, $ np $ and $ n(1 - p) $ are both less than 5.$ \circ $ yes, $ np $ and $ n(1 - p) $ are both greater than 5.$ \circ $ no, $ n(1 - p) $ is less than 5.$ \circ $ no, $ np $ is less than 5.\
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6. - / 10 points\
mendstat15cr 7.5.011.mi.sa.s.\
this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.\
tutorial exercise\
random samples of size $ n = 85 $ were selected from a binomial population with $ p = 0.8 $. use the normal distribution to approximate the following probability.$ p(0.75 \leq \hat{p} \leq 0.88) $\
step 1\
to check whether the normal approximation to the binomial distribution is appropriate for this case, we confirm $ np 5 $ and $ nq 5 $, where sample size $ n = 85 $ and mean $ p = 0.8 $ are given, and $ q = 1 - p $.\
find $ np $ and $ nq $.$ np = 85(0.8) $$ = $$ nq = 85(1 - 0.8) $$ = $\
because $ np $? 5 and $ nq $? 5, the normal approximation to the binomial distribution $ \text{--select--} $ appropriate.\
\
7. - / 13 points

Question

is it appropriate to use the normal distribution to approximate the sampling distribution of $ \hat{p} $ for the following?$ n = 350, p = 0.99 $$ \circ $ no, $ np $ and $ n(1 - p) $ are both less than 5.$ \circ $ yes, $ np $ and $ n(1 - p) $ are both greater than 5.$ \circ $ no, $ n(1 - p) $ is less than 5.$ \circ $ no, $ np $ is less than 5.\
\
6. - / 10 points\
mendstat15cr 7.5.011.mi.sa.s.\
this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.\
tutorial exercise\
random samples of size $ n = 85 $ were selected from a binomial population with $ p = 0.8 $. use the normal distribution to approximate the following probability.$ p(0.75 \leq \hat{p} \leq 0.88) $\
step 1\
to check whether the normal approximation to the binomial distribution is appropriate for this case, we confirm $ np > 5 $ and $ nq > 5 $, where sample size $ n = 85 $ and mean $ p = 0.8 $ are given, and $ q = 1 - p $.\
find $ np $ and $ nq $.$ np = 85(0.8) $$ = $$ nq = 85(1 - 0.8) $$ = $\
because $ np $? 5 and $ nq $? 5, the normal approximation to the binomial distribution $ \text{--select--} $ appropriate.\
\
7. - / 13 points

Accepted Answer

# Explanation:
## Step1: Calculate $ np $
We know that $ n = 85 $ and $ p = 0.8 $. To find $ np $, we multiply $ n $ and $ p $.
$ np = 85\times0.8 = 68 $

## Step2: Calculate $ nq $
First, find $ q $ where $ q = 1 - p $. So $ q = 1 - 0.8 = 0.2 $. Then multiply $ n $ and $ q $.
$ nq = 85\times(1 - 0.8)=85\times0.2 = 17 $

Now, check if $ np>5 $ and $ nq>5 $. Since $ 68>5 $ and $ 17>5 $, the normal approximation to the binomial distribution is appropriate.

# Answer:
For $ np $: $ 68 $
For $ nq $: $ 17 $
And the normal approximation is appropriate.

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate \( np \)

Step2: Calculate \( nq \)

Answer: