Question

1/ A particular fruit's weights are normally distributed, with a mean of 352 grams and a standard deviation of 28 grams.
If you pick 9 fruits at random, then 9% of the time, their mean weight will be greater than how many grams?
Give your answer to the nearest gram.

2/A manufacturer knows that their items have a lengths that are skewed right, with a mean of 7.5 inches, and standard deviation of 0.9 inches.
If 50 items are chosen at random, what is the probability that their mean length is greater than 7.3 inches?
(Round answer to four decimal places)

3/A population of values has a normal distribution with μ=117.8μ=117.8 and σ=83.5σ=83.5. You intend to draw a random sample of size n=12n=12.
Find the probability that a single randomly selected value is less than 91.3.
P(X < 91.3) = ........?
Find the probability that a sample of size n=12n=12 is randomly selected with a mean less than 91.3.
P(M < 91.3) = ........?
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.

4/A population has parameters μ=162.8μ=162.8 and σ=3.7σ=3.7. You intend to draw a random sample of size n=237n=237.
What is the mean of the distribution of sample means?
μ¯x=μx¯= .....
What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
σ¯x=σx¯= ....

Answer 1