Question

The heights of kindergarten children are approximately normally distributed with the following. (Give your answers correct to four decimal places.) μ = 50 and σ = 2.2 inches (a) If an individual kindergarten child is selected at random, what is the probability that he or she has a height between 47.5 and 52.5 inches? (b) A classroom of 16 of these children is used as a sample. What is the probability that the class mean x is between 47.5 and 52.5 inches? (c) If an individual kindergarten child is selected at random, what is the probability that he or she is taller than 52 inches? (d) A classroom of 16 of these kindergarten children is used as a sample. What is the probability that the class mean x is greater than 52 inches?

Answer #1

mean = 50 , s = 2.2

By using central limit theorem,

z = (x - mean)/sigma

a)

P(47.5 < x < 52.5)

= P((47.5 - 50)/2.2 < z < (52.5 - 50)/2.2)

= P(-1.14 < z < 1.14)

= 0.8721 - 0.1279

= 0.7442

b)

Here, n =16

P(47.5 < x < 52.5)

= P((47.5 - 50)/(2.2/sqrt(16)) < z < (52.5 -
50)/(2.2/sqrt(16)))

= P(-4.55 < z < 4.55)

= 1- 0

= 1

c)

P(x> 52)

= 1 - P(z< (52 - 50)/2.2)

= 1 - P(z < 0.91)

= 1 - 0.8183

= 0.1817

d)

Here, n =16

P(x> 52)

= 1 - P(z< (52 - 50)/(2.2/sqrt(16))

= 1 - P(z < 3.64)

= 1 - 0.9999

= 0.0001

Kindergarten children have heights that are approximately
normally distributed about a mean of 39 inches and a standard
deviation of 2 inches. If a random sample of 19 is taken, what is
the probability that the sample of kindergarten children has a mean
height of less than 39.50 inches? (Round your answer to four
decimal places.)

Kindergarten children have heights that are approximately
normally distributed about a mean of 39 inches and a standard
deviation of 2 inches. If a random sample of 34 is taken, what is
the probability that the sample of kindergarten children has a mean
height of less than 39.50 inches? (Round your answer to four
decimal places.)
*PLEASE DOUBLE CHECK YOUR WORK, I HAVE BEEN GETTING ALOT OF
WRONG ANSWERS LATELY*

The heights of kindergarten children are approximately
normally distributed with a mean height of 39 inches and a standard
deviation of 2 inches. If a first-time kindergarten teacher finds
the average height for the 20 students in her class is 40.3 inches,
would that be unusual? Explain.
ANSWER 0.0018
please show step by step ! thank you

The age of children in kindergarten on the first day of school
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decimal places if possible.
The mean of this distribution is _______
The standard deviation is _______
The probability that the the child will be older than 5 years
old? _______
The probability that the child will be between 5.01 and 5.51
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If...

In a large city, the heights of 10-year-old children are
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standard deviation of 3.7 inches.
(a) What is the probability that a randomly chosen 10-year-old
child has a height that is less than than 50.35 inches? Round your
answer to 3 decimal places.
(b) What is the probability that a randomly chosen 10-year-old
child has a height that is more than 53.2 inches? Round your answer
to 3 decimal places.

The heights of kindergarten children are distributed with a
mean, , of 39 and a standard deviation, , of 2. Use a sample size,
, of 30.
Find mu subscript top enclose x end subscript
4 points
QUESTION 19
Find sigma subscript top enclose x end subscript
4 points
QUESTION 20
Find: P(38<= x <= 40)

Suppose the heights of 18-year-old men are approximately
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Suppose the heights of 18-year-old men are approximately
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decimal places.)

Suppose the heights of 18-year-old men are approximately
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(a) What is the probability that an 18-year-old man selected at
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(b) If a random sample of eleven 18-year-old men is selected, what
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The heights of women in the U.S. have been found to be
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a) What percent of women are taller than 64.61 inches?
probability =
b) What percent of women are shorter than 61.35 inches?
probability =
c) What percent have heights between 61.35 and 64.61 inches?
probability =
Note: Do NOT input probability responses as percentages; e.g.,
do NOT input 0.9194 as 91.94.

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