(a) Is it appropriate to use the normal approximation to find the probability that less than of the individuals in the sample hold multiple jobs? If so, find the probability, If not, explain why not.
nt
is not appropriate to use the normal curve, since
3.4 10,

Part 2 of 5
(b) A new sample of 336 employed adults is chosen. Find the probability that less than of the individuals in this sample hold multiple jobs. Round the answer to at least four decimal places as needed.

The probability that less than of the individuals in this sample hold multiple jobs is 0.8964 .

Part 3 of 5
© Find the probability that more than of the individuals in the sample of 336 hold multiple jobs. Round the answer to at least four decimal places as needed.

The probability that more than of individuals in the sample of 336 hold multiple jobs is 0.1036 .

Part 4 of 5
(d) Find the probability that the proportion of individuals in the sample of 336 who hold multiple jobs is between 0.054 and 0.10 . Round the answer to at least four decimal places as needed.

The probability that the proportion of individuals in the sample of 336 hold multiple jobs is between 0.054 and 0.10 is 0.3683 .

Part: 4/5

Part 5 of 5
(e) Using a cutoff of 0.05 , would it be unusual if less than of the individuals in the sample of 336 held multiple jobs? Round the answer to at least four decimal places as needed.
it (Choose one) be ugusual if less than of the individuals in the sample of 336 held multiple jobs, since the probability is .

Ask by Huang Schwartz. in the United States

Feb 11,2025

Question

(a) Is it appropriate to use the normal approximation to find the probability that less than of the individuals in the sample hold multiple jobs? If so, find the probability, If not, explain why not.
nt
is not appropriate to use the normal curve, since
3.4 10,

Part 2 of 5
(b) A new sample of 336 employed adults is chosen. Find the probability that less than of the individuals in this sample hold multiple jobs. Round the answer to at least four decimal places as needed.

The probability that less than of the individuals in this sample hold multiple jobs is 0.8964 .

Part 3 of 5
© Find the probability that more than of the individuals in the sample of 336 hold multiple jobs. Round the answer to at least four decimal places as needed.

The probability that more than of individuals in the sample of 336 hold multiple jobs is 0.1036 .

Part 4 of 5
(d) Find the probability that the proportion of individuals in the sample of 336 who hold multiple jobs is between 0.054 and 0.10 . Round the answer to at least four decimal places as needed.

The probability that the proportion of individuals in the sample of 336 hold multiple jobs is between 0.054 and 0.10 is 0.3683 .

Part: 4/5

Part 5 of 5
(e) Using a cutoff of 0.05 , would it be unusual if less than of the individuals in the sample of 336 held multiple jobs? Round the answer to at least four decimal places as needed.
it (Choose one) be ugusual if less than of the individuals in the sample of 336 held multiple jobs, since the probability is .

Ask by Huang Schwartz. in the United States

Feb 11,2025

UpStudy AI · Accepted Answer

We are told that the population proportion of employed adults who hold multiple jobs is p = 0.05 (that is, 5% of adults hold multiple jobs). (All numerical answers below assume that p = 0.05.) In several parts of the problem a “sample proportion” is considered. In part (a) the sample size is small – in fact, it is chosen so that np = 68 × 0.05 = 3.4 (and n[1 – p] = 68 × 0.95 = 64.6) – and in parts (b)–(e) a larger sample of n = 336 is used.

Below is one acceptable solution.

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Part (a)

For using the normal approximation to the binomial (or equivalently to the sampling distribution of p̂) the rule of thumb is that both np and n(1 – p) should be at least 10. In the first situation the sample size is such that

np = 68 × 0.05 = 3.4  and  n(1 – p) = 68 × 0.95 = 64.6.

Since np = 3.4 is less than 10, the normal approximation is not appropriate for a sample of this size.
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Part (b)

Now a new sample of n = 336 employed adults is chosen. For the sampling distribution of the sample proportion p̂ we have

Mean = p = 0.05 and Standard deviation = σₚ̂ = √[p(1 – p)/n] = √[0.05 × 0.95/336] ≈ 0.01189.

We wish
(a) It is not appropriate to use the normal approximation because $$ np = 3.4 $$ is less than 10. (b) The probability that less than $$ 6.5\% $$ of the individuals in the sample hold multiple jobs is 0.8964. (c) The probability that more than $$ 6.5\% $$ of the individuals in the sample hold multiple jobs is 0.1036. (d) The probability that the proportion of individuals in the sample holds multiple jobs between 0.054 and 0.10 is 0.3683. (e) It would not be unusual if less than $$ 2.5\% $$ of the individuals in the sample held multiple jobs, since the probability is 0.1036.

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