Consider two independent binomial experiments. In the first one, 86 trials had 51 successes. In the second one, 83 trials had 21 successes. Find the point estimate for a 95% confidence interval. Use at least 4 decimal places.

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Consider two independent binomial experiments. In the first one, 86 trials had 51 successes. In the second
one, 83 trials had 21 successes.
Find the point estimate for a 95% confidence interval. Use at least 4 decimal places.
Transcribed Image Text:Consider two independent binomial experiments. In the first one, 86 trials had 51 successes. In the second one, 83 trials had 21 successes. Find the point estimate for a 95% confidence interval. Use at least 4 decimal places.
HU
According to a study, the length of pregnancy has unknown distribution with a mean of 274 days and a
standard deviation of 14.8 days. Let X be the length of pregnancy for a randomly selected female and let
X be the average length of pregnancy for a random sample of size 11.
1. Describe the probability distribution of X and state its parameters μ and σ:
or (μ= 270, 0 = 14✓ 0³
and find the probability that the length of pregnancy for a randomly selected female is more than 313
days.
X~ unknown
0.0 x (Round the answer to 4 decimal places)
Note: If it is not possible to compute, type "DNE"
2. Explain why the Central Limit Theorem cannot be used
the sample size is small (n<30) and the distribution of the original population is unknown
Transcribed Image Text:HU According to a study, the length of pregnancy has unknown distribution with a mean of 274 days and a standard deviation of 14.8 days. Let X be the length of pregnancy for a randomly selected female and let X be the average length of pregnancy for a random sample of size 11. 1. Describe the probability distribution of X and state its parameters μ and σ: or (μ= 270, 0 = 14✓ 0³ and find the probability that the length of pregnancy for a randomly selected female is more than 313 days. X~ unknown 0.0 x (Round the answer to 4 decimal places) Note: If it is not possible to compute, type "DNE" 2. Explain why the Central Limit Theorem cannot be used the sample size is small (n<30) and the distribution of the original population is unknown
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