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pochemuha
3 years ago
8

Describe the sampling distribution of Phat. Assume the size of the Population is 25,000. N = 500 P = 0.4 Determine the Mean of t

he sampling distribution of Phat. Determine the standard deviation of the sampling distribution of Phat.

Mathematics
1 answer:
PIT_PIT [208]3 years ago
5 0

Answer:

0.022

Step-by-step explanation:

Given that :

Population size = 25000

n = 500 ; p = 0.4

Size of random sample (n) = 500

5% of population size : 0.05 * 25000 = 1250

Distribution is normally distributed since n < 5% of population size

Hence, the mean of the distribution = p = 0.4

Standard deviation = √((pq) /n)

q = 1 - p ; q = 1 - 0. 4 = 0.6

Standard deviation = √((0.4 * 0.6) /500)

Standard deviation = 0.0219089

= 0.022

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Answer:

a) P(a > 80) = 0.323

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c) The 95% confidence interval expresses that the mean of the distribution can always be found in the given range, with a 95% confidence level.

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X ~ (45, 4)

Y ~ (32, 2.5)

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a) Probability that the time required to complete both of those steps will exceed 80 min = P(a > 80)

This is a normal distribution problem

We then standardize 80 min time

The standardized score for any value is the value minus the mean then divided by the standard deviation.

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To determine the probability the time required to complete both of those steps will exceed 80 min = P(a > 80) = P(z > 0.46)

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We need to obtain the margin of error

Margin of error = (critical value) × (standard error of the sample)

Critical value for a 95% confidence interval = critical value for a significance level of 5% = t(15-1, 0.05/2) = 2.145 (using the t-score since information on the population mean and standard deviation isn't known)

Standard error for the sample of sum of times = (standard deviation of the sum of times)/√n = (6.5/√15) = 1.678

Margin of error = 2.145 × 1.678 = 3.60

Limits of the confidence interval = (Sample mean ± margin of error)

Lower limit of the confidence interval = (Sample mean - margin of error) = 77 - 3.60 = 73.40

Upper limit of the confidence interval = 77 + 3.60 = 80.60

The confidence interval = (73.40, 80.60)

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