Question

A variable of a population has a mean of ?=150 and a standard deviation of ?=21. a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean __ and standard deviation __

A company sells sunscreen in 500 milliliters (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean ?=497 ml and a standard deviation ?=5 ml. Suppose a store that sells this sunscreen advertises a sale for 5 tubes for the price of 4. Consider the average amount of lotion from an SRS of 5 tubes of sunscreen and find: (a) The standard deviation of the average, ?¯ : (b) The probability that the average amount of sunscreen from 5 tubes will be less than 489 ml. Answer:

Assume that women's weights are normally distributed with a mean given by ?=143 lb and a standard deviation given by ?=29 lb. (a) If 1 woman is randomly selected, find the probabity that her weight is between 113 lb and 179 lb (b) If 6 women are randomly selected, find the probability that they have a mean weight between 113 lb and 179 lb (c) If 63 women are randomly selected, find the probability that they have a mean weight between 113 lb and 179 lb

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 112 cm and a standard deviation of 4.8 cm. A. Find the probability that one selected subcomponent is longer than 114 cm. Probability = B. Find the probability that if 3 subcomponents are randomly selected, their mean length exceeds 114 cm. Probability = C. Find the probability that if 3 are randomly selected, all 3 have lengths that exceed 114 cm. Probability =

Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112. (a) If 1 man is randomly selected, find the probability that his score is at least 587. (b) If 15 men are randomly selected, find the probability that their mean score is at least 587. 15 randomly selected men were given a review course before taking the SAT test. If their mean score is 587, is there strong evidence to support the claim that the course is actually effective?

Answer #1

Question: A variable of a population has a mean of ?=150 and a standard deviation of ?=21. a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean __ and standard deviation __

Answer: We know that if the repeated samples of size 49 taken
from the population where population mean is 150 and the population
standard deviation is 21 then is mean of all sample means is same
as population mean and the standard deviation of all sample mean is
given by ?/ **(√** n). Therefore,

Mean of sample mean = 150

Standard deviation of sample means = ?/ **(√** n) =
21/**√**49 = 21/7 = 3

Weights of men are normally distributed with a mean of 189 lb
and a standard deviation of 39 lb. If 20 men are randomly selected,
find the probability that they have weights with a mean between 200
lb and 230 lb.

Scores for men on the verbal portion of the SAT-I test are
normally distributed with a mean of 509 and a standard deviation of
112.
(a) If 1 man is randomly selected, find the probability that his
score is at least 572.5.
(b) If 10 men are randomly selected, find the probability that
their mean score is at least 572.5.

Assume that the population of weights of men is normally
distributed with mean 172 lb and standard deviation 29 lb. a. If an
individual man is randomly selected, find the probability that his
weight will be greater than 175 lb. (Round to four decimal places
as needed.) b. Find the probability that 20 randomly selected men
will have a mean weight that is greater than 175 lb. (Round to four
decimal places as needed.) show work

Scores for men on the verbal portion of the SAT-I test are
normally distributed with a mean of 509 and a standard deviation of
112.
(a) If 11 man is randomly selected, find the
probability that his score is at least 579.5
(b) If 13 men are randomly selected, find the
probability that their mean score is at least 579.5
13 randomly selected men were given a review course before taking
the SAT test. If their mean score is 579.5, is there...

Assume that the population of weights of men is normally
distributed with mean 172 lb and standard deviation 29 lb.
a. If an individual man is randomly selected,
find the probability that his weight will be greater than 175 lb.
(Round to four decimal places as needed.)
b. Find the probability that 20 randomly selected men will have
a mean weight that is greater than 175 lb. (Round to four decimal
places as needed.)
Please show all work as if...

Assume that women's weights are normally distributed with a mean
given by ?=143 lb and a standard deviation given by ?=29 lb.
(a) If 1 woman is randomly selected, find the probabity that her
weight is between 113 lb and 173 lb
(b) If 5 women are randomly selected, find the probability that
they have a mean weight between 113 lb and 173 lb
(c) If 82 women are randomly selected, find the probability that
they have a mean weight...

A company sells sunscreen in 500 milliliter (ml) tubes. In fact,
the amount of lotion in a tube varies according to a normal
distribution with mean ?=498 ml and standard deviation ?=5 ml.
Suppose a store which sells this sunscreen advertises a sale for 5
tubes for the price of 4. Consider the average amount of lotion
from a SRS of 5 tubes of sunscreen and find:
(a) The standard deviation of the average, ?¯ :
(b) The probability that...

13) Weights of population of men has the mean of 170
pounds and the standard deviation of 27 pounds. Suppose 81 men from
this population are randomly selected for a certain study
The distribution of the sample mean weight is
a)exactly normal, mean 170 lb, standard deviation 27lb
b) approximately Normal, mean 170 lb, standard deviation 0.3
lb
c)approximately Normal, mean 170 lb, standard deviation
3 lb
d)approximately Normal, mean equal to the observed value of the
sample mean, standard deviation 27...

The mean of a normally distributed data set is 112, and the
standard deviation is 18.
a) Use the Empirical Rule to find the probability
that a randomly-selected data value is greater than 130.
b) Use the Empirical Rule to find the probability
that a randomly-selected data value is greater than 148.
A psychologist wants to estimate the proportion of people in a
population with IQ scores between 85 and 130. The IQ scores of this
population are normally distributed...

Average height of men is normally distributed with mean height
of 160 cm and standard deviation of 5 cm. If a sample of 9 men are
randomly selected from this population, find the probability that
the mean is between 155 cm and 160 cm. Question 20 options: 0.3412
0.50 0.0013 0.4987 0.5821

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