A population of values has a normal distribution with 118 5 and 33 6 You intend to draw a random sample of size n 72 What is the mean of the distribution of sample means What is the standard deviation of the distribution of sample means (Report answer accurate to 2 decimal places ) x A population of values has a normal distribution with 82 1 and 10 9 You intend to draw a random sample of size n 226 Find the probability that a single randomly selected value is less than 82 6 P ( X 82 6) Find the probability that a sample of size n 226n 226 is randomly selected with a mean less than 82 6 P ( M 82 6) Enter your answers as numbers accurate to 4 decimal places Answers obtained using exact z scores or z scores rounded to 3 decimal places are accepted Which of the following statements are true I The sampling distribution of xx has standard deviation nn even if the population is not normally distributed II The sampling distribution of xx is normal if the population has a normal distribution III When nn is large, the sampling distribution of xx is approximately normal even if the the population is not normally distributed I and II I and III II and III I, II, and III None of the above gives the complete set of true responses A manufacturer knows that their items have a normally distributed length, with a mean of 19 3 inches, and standard deviation of 5 5 inches If 7 items are chosen at random, what is the probability that their mean length is less than 23 inches A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14 7 years, and standard deviation of 1 6 years If you randomly purchase 25 items, what is the probability that their mean life will be longer than 14 years A particular fruit's weights are normally distributed, with a mean of 470 grams and a standard deviation of 36 grams If you pick 25 fruit at random, what is the probability that their mean weight will be between 453 grams and 465 grams A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3 4 years, and standard deviation of 0 8 years If 5 items are picked at random, 6 of the time their mean life will be less than how many years Give your answer to one decimal place

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A population of values has a normal distribution with =118.5 and =33.6. You intend to draw a random sample of size n=72. What is the mean of the distribution of sample means? = What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) x=
A population of values has a normal distribution with =82.1 and =10.9. You intend to draw a random sample of size n=226. Find the probability that a single randomly selected value is less than 82.6. P(X < 82.6) = Find the probability that a sample of size n=226n=226 is randomly selected with a mean less than 82.6. P(M < 82.6) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Which of the following statements are true? I. The sampling distribution of xx has standard deviation nn even if the population is not normally distributed. II. The sampling distribution of xx is normal if the population has a normal distribution. III. When nn is large, the sampling distribution of xx is approximately normal even if the the population is not normally distributed.

A manufacturer knows that their items have a normally distributed length, with a mean of 19.3 inches, and standard deviation of 5.5 inches. If 7 items are chosen at random, what is the probability that their mean length is less than 23 inches?
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.7 years, and standard deviation of 1.6 years. If you randomly purchase 25 items, what is the probability that their mean life will be longer than 14 years?
A particular fruit's weights are normally distributed, with a mean of 470 grams and a standard deviation of 36 grams. If you pick 25 fruit at random, what is the probability that their mean weight will be between 453 grams and 465 grams
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.4 years, and standard deviation of 0.8 years. If 5 items are picked at random, 6% of the time their mean life will be less than how many years? Give your answer to one decimal place.