Normal Probability Distribution Archives - Page 4 of 16

Normal Probability Distribution

The mean weight of an adult is 65 kilograms with a standard deviation of 9 kilograms. If 100 adults are randomly selected, what is the probability that the sample mean would be less than 66.8 kilograms? Round your answer to four decimal places.

Answer: Given Data: The Population Mean $(μ) = 65$ The Population Standard Deviation $(σ) = 9$ The Sample Size $(n) = 100$ Solution: The probability that the sample mean would be less than 66.8…

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The mean weight of an adult is 70 kilograms with a standard deviation of 12 kilograms. If 150 adults are randomly selected, what is the probability that the sample mean would be less than 72.5 kilograms? Round your answer to four decimal places.

Answer: Given Data: The Population Mean $(μ) = 70$ The Population Standard Deviation $(σ) = 12$ The Sample Size $(n) = 150$ Solution: The probability that the sample mean would be less than 72.5…

Normal Probability Distribution

The mean weight of an adult is 68 kilograms with a standard deviation of 10 kilograms. If 128 adults are randomly selected, what is the probability that the sample mean would be less than 70.3 kilograms? Round your answer to four decimal places.

Answer: Given Data: The Population Mean $(μ) = 68$ The Population Standard Deviation $(σ) = 10$ The Sample Size $(n) = 128$ Solution: The probability that the sample mean would be less than 70.3 kilograms:…

Normal Probability Distribution

The amount of weight a high school student carries in his or her bookbag follows a normal distribution with a standard deviation of σ = 2.5 pounds. Suppose a random sample of 22 bookbags produced a mean of 15 pounds. Construct a 95% confidence interval to estimate the mean bookbag weight for all high school students.

Answer:Given: Sample Mean $(x \bar{)} = 15$ Population Standard Deviation $(σ) = 2.5$ Sample Size $(n) = 22$ Confidence Interval Level $(C I) = 95 %$ Solution: The level of significance $(α) :$ $ \alpha = 1 – 0.95…

Normal Probability Distribution

The amount of weight a high school student carries in his or her bookbag follows a normal distribution with a standard deviation of σ = 3 pounds. Suppose a random sample of 30 bookbags produced a mean of 14 pounds. Construct a 95% confidence interval to estimate the mean bookbag weight for all high school students.

Answer:Given: Sample Mean $(x \bar{)} = 14$ Population Standard Deviation $(σ) = 3$ Sample Size $(n) = 30$ Confidence Interval Level $(C I) = 95 %$ Solution: The level of significance $(α) :$ $ \alpha = 1 – 0.95…

Normal Probability Distribution

The amount of weight a high school student carries in his or her bookbag follows a normal distribution with a standard deviation of σ = 2 pounds. Suppose a random sample of 20 bookbags produced a mean of 13 pounds. Construct a 95% confidence interval to estimate the mean bookbag weight for all high school students.

Answer:Given: Sample Mean $(x \bar{)} = 13$ Population Standard Deviation $(σ) = 2$ Sample Size $(n) = 20$ Confidence Interval Level $(C I) = 95$ Solution: The level of significance $(α) :$ $α = 1 - 0.95 = 0.05$ …

Normal Probability Distribution

Standard normal proportion. Use table B to find the proportion of a standard normal distribution that is: (a) below -1.42 (b) above 1.42 (c) below 1.25 (d) between 1.42 and 1.25

Answer : A) The probability that z is below −1.42 : $P (z < - 1.42) = 0.0778$ B) The probability that z is above 1.42 : $P (z > 1.42) = 0.0778$ C) The probability that z is below 1.25 : $P(z…

Normal Probability Distribution

The mean number of words per minute (WPM) typed by a speed typist is 73 with a variance of 144. What is the probability that the sample mean would differ from the population mean by greater than 0.6 WPM if 77 speed typists are randomly selected?

Answer : Given information : The population mean $(μ) = 73$ The population standard deviation $(σ) = \sqrt{σ^{2}} = \sqrt{144} = 12$ The sample size $(n) = 77$ Solution : → The probability that the sample mean would differ from…

Normal Probability Distribution

Optimal Eats steamer has a mean time before failure of 32 months with a standard deviation of 5 months, and the failure times are normally distributed. What should be the warranty period, in months, so that the manufacturer will not have more than 10% of the steamers returned?

Answer : Given info : The population mean $(μ) = 32$ The population standard deviation $(σ) = 5$ Solution : The Warranty Period for Less Than 10% Failure Rate: $∴ P (x < z) = 0.10$ $∴ z = - 1.282$ $$\text{Now,…

Normal Probability Distribution

One component of college expenses is your book costs. A sample of students indicates that the average book cost for a semester is 260 dollars and the standard deviation is 50 dollars. If nothing is known about the shape of the book cost distribution, what percentage of the students would have book costs that exceeded 460 dollars?

Answer : Given inf : The population mean $(μ) = 260$ The population standard deviation $(σ) = 50$ Solution : The percentage of the students would have book costs that exceeded 460 dollars : $$\therefore P(x > 460) = P\left(…