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Kryger [21]
3 years ago
6

The heights of a random sample of 100 women are recorded. The sample mean is 65.3 inches and the sample standard deviation is 3

inches. whicho of the following is an approximate 95% confidence interval for the population mean?A. 65.3 + (2)(0.03) B. 65.3 + (2)(.3) C. 65.3 + (2)(3) D. 65.3 + (2)(30)
Mathematics
2 answers:
Keith_Richards [23]3 years ago
8 0

Answer: B. 65.3\pm(2)(0.3)

Step-by-step explanation:

The confidence interval for the population mean is given by :-

\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

Given : Sample size : n= 100

Sample mean : \overline{x}=65.3\text{ inches}

Standard deviation: \sigma=3 \text{ inches}

Level of confidence = 0.95

Significance level : \alpha=1-0.95=0.05

Critical value : z_{\alpha/2}=1.96

Then, 95% confidence interval for the population mean will be :-

65.3\pm (1.96)\dfrac{3}{\sqrt{100}}\\\\\approx65.3\pm(2)(\dfrac{3}{10})=65.3\pm(2)(0.3)

yawa3891 [41]3 years ago
3 0

Answer:

The answer for this Question is B.

Step-by-step explanation:

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