Question
In: Statistics and Probability
1.) Suppose heights of two-year-olds are normally distributed with a mean of 30 inches and a...
1.) Suppose heights of two-year-olds are normally distributed with a mean of 30 inches and a standard deviation of 3.5 inches.
a) What is the probability that one two-year-old will be shorter than 28 inches?
b) If random samples of size n = 40 two-year-olds are selected, what is the approximate shape, mean, and standard deviation of the sampling distribution of sample means?
c) What is the probability that the sample mean of these 40 two-year-olds will be shorter than 28 inches? Why is the probability in part c) so much smaller than the probability in part a)?
d) What is the probability that the sample mean of these 40 two-year-olds will be taller than 31 inches?
Solutions
orchestra answered 1 year agoRelated Solutions
Suppose the heights of males on campus are normally distributed with a mean of 69 inches...
Suppose the heights of males on campus are normally distributed
with a mean of 69 inches and standard deviation of 2.5 inches. You
plan to choose a random sample of 14 males from the student
directory.
a. What is the probability the mean height for your sample will
be greater than 70.5 inches?
b. The sample size you used was fairly small. Does this affect
the validity of the probability you calculated in (a)?
1. Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and...
1. Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 71 inches and standard
deviation 5 inches.
(a) What is the probability that an 18-year-old man selected at
random is between 70 and 72 inches tall? (Round your answer to four
decimal places.)
(b) If a random sample of twenty-three 18-year-old men is selected,
what is the probability that the mean height x is between
70 and 72 inches? (Round your answer to four decimal places.)
(c)...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard...
Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 68 inches and standard deviation 5
inches. (a) What is the probability that an 18-year-old man
selected at random is between 67 and 69 inches tall? (Round your
answer to four decimal places.) (b) If a random sample of twelve
18-year-old men is selected, what is the probability that the mean
height x is between 67 and 69 inches? (Round your answer to four
decimal places.) (c) Compare...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 67 inches and standard...
Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 67 inches and standard
deviation 3 inches.
b) If a random sample of thirteen 18-year-old men is selected,
what is the probability that the mean height x is between
66 and 68 inches? (Round your answer to four decimal places.)
_________________
Let x represent the dollar amount spent on supermarket
impulse buying in a 10-minute (unplanned) shopping interval. Based
on a certain article, the mean of the x...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard...
Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 71 inches and standard
deviation 5 inches.
(a) What is the probability that an 18-year-old man
selected at random is between 70 and 72 inches tall? (Round your
answer to four decimal places.)
(b) If a random sample of twenty-four 18-year-old men is
selected, what is the probability that the mean height x
is between 70 and 72 inches? (Round your answer to four decimal
places.)
(c) Compare...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 72 inches and standard...
Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 72 inches and standard
deviation 5 inches.
1. What is the probability that an 18-year-old man selected at
random is between 71 and 73 inches tall? (Round your answer to four
decimal places.)
__________________
2. If a random sample of fourteen 18-year-old men is selected, what
is the probability that the mean height x is between 71
and 73 inches? (Round your answer to four decimal places.)
_________________...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 67 inches and standard...
Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 67 inches and standard
deviation 1 inches.
(a) What is the probability that an 18-year-old man selected at
random is between 66 and 68 inches tall? (Round your answer to four
decimal places.)
(b) If a random sample of twenty-nine 18-year-old men is selected,
what is the probability that the mean height x is between
66 and 68 inches? (Round your answer to four decimal places.)
(c) Compare...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard...
Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 66 inches and standard
deviation 1 inches.
(a) What is the probability that an 18-year-old man selected at
random is between 65 and 67 inches tall? (Round your answer to four
decimal places.)
(b) If a random sample of twenty-six 18-year-old men is selected,
what is the probability that the mean height x is between
65 and 67 inches? (Round your answer to four decimal places.)
(c) Compare...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard...
Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 69 inches and standard
deviation 1 inches.
(a) What is the probability that an 18-year-old man selected at
random is between 68 and 70 inches tall? (Round your answer to four
decimal places.)
(b) If a random sample of fifteen 18-year-old men is selected, what
is the probability that the mean height x is between 68
and 70 inches? (Round your answer to four decimal places.)
(c) Compare...
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard...
Suppose the heights of 18-year-old men are approximately
normally distributed, with mean 71 inches and standard
deviation 5 inches.
(a) What is the probability that an 18-year-old man selected at
random is between 70 and 72 inches tall? (Round your answer to four
decimal places.)
(b) If a random sample of eighteen 18-year-old men is selected,
what is the probability that the mean height x is between
70 and 72 inches? (Round your answer to four decimal places.)
(c) Compare...
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