The mean life of a television set is 119 months with a standard deviation of 13 months. If a sample of 67 televisions is randoml
y selected, what is the probability that the sample mean would differ from the true mean by less than 2 months? Round your answer to four decimal places.
1 answer:
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Answer:
The area of the shaded region is 42.50 cm².
Step-by-step explanation:
Consider the figure below.
The radius of the circle is, <em>r</em> = 5 cm.
The sides of the rectangle are:
<em>l</em> = 11 cm
<em>b</em> = 11 cm.
Compute the area of the shaded region as follows:
Area of the shaded region = Area of rectangle - Area of circle
Thus, the area of the shaded region is 42.50 cm².
Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - <em>α</em>)% confidence interval for population mean μ is:
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
<em>n</em>₁ = 25
<em>n</em>₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
Width for n = 64:
Thus, the sample consisting of 64 data values would give a greater precision