Question

1. Assume that *x* has a normal distribution with the
specified mean and standard deviation. Find the indicated
probability. (Round your answer to four decimal places.)

*μ* = 50; *σ* = 15

*P*(40 ≤ *x* ≤ 47) =

2. Coal is carried from a mine in West Virginia to a power plant
in New York in hopper cars on a long train. The automatic hopper
car loader is set to put 56 tons of coal into each car. The actual
weights of coal loaded into each car are *normally
distributed*, with mean *μ* = 56 tons and standard
deviation *σ* = 0.9 ton.

(a) What is the probability that one car chosen at random will have less than 55.5 tons of coal? (Round your answer to four decimal places.)

(b) What is the probability that 23 cars chosen at random will
have a mean load weight *x* of less than 55.5 tons of coal?
(Round your answer to four decimal places.)

(c) Suppose the weight of coal in 23 cars selected at random had
an average *x* of less than 55.5 tons. Would that fact make
you suspect that the loader had slipped out of adjustment? Why?

a. Yes, the probability that this deviation is random is very small.

b. Yes, the probability that this deviation is random is very large.

c. No, the probability that this deviation is random is very small.

d. No, the probability that this deviation is random is very large.

Answer #1

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 56 tons of coal into each car. The actual
weights of coal loaded into each car are normally distributed, with
mean μ = 56 tons and standard deviation σ = 0.8 ton. (a) What is
the probability that one car chosen at random will have less than
55.5...

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 51 tons of coal into each car. The actual
weights of coal loaded into each car are normally distributed, with
mean μ = 51 tons and standard deviation σ = 0.5 ton.
(a) What is the probability that one car chosen at random will
have less than 50.5...

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 89 tons of coal into each car. The actual
weights of coal loaded into each car are normally distributed, with
mean μ = 89 tons and standard deviation σ = 1 ton.
(a) What is the probability that one car chosen at random will
have less than 88.5...

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 79 tons of coal into each car. The actual
weights of coal loaded into each car are normally distributed, with
mean μ = 79 tons and standard deviation σ = 0.7 ton. (a) What is
the probability that one car chosen at random will have less than
78.5...

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 68 tons of coal into each car. The actual
weights of coal loaded into each car are normally distributed, with
mean μ = 68 tons and standard deviation σ = 1.2 ton. (a) What is
the probability that one car chosen at random will have less than
67.5...

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 57 tons of coal into each car. The actual
weights of coal loaded into each car are normally
distributed, with mean μ = 57 tons and standard
deviation σ = 0.6 ton.
(a) What is the probability that one car chosen at random will
have less than 56.5...

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 61 tons of coal into each car. The actual
weights of coal loaded into each car are normally
distributed, with mean μ = 61 tons and standard
deviation σ = 0.5 ton.
(a) What is the probability that one car chosen at random will
have less than 60.5...

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to pull 73 tons of coal into each car. The actual
weights of coal loaded into each car are normally distributed, with
mean ? = 73 tons and standard deviation ? = 0.9 ton. (a) What is
the probability that one car chosen at random will have less than
72.5...

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 88 tons of coal into each car. The actual
weights of coal loaded into each car are normally
distributed, with mean μ = 88 tons and standard
deviation σ = 1.3 ton.
(a) What is the probability that one car chosen at random will
have less than 87.5...

Coal is carried from a mine in West Virginia to a power plant in
New York in hopper cars on a long train. The automatic hopper car
loader is set to put 62 tons of coal into each car. The actual
weights of coal loaded into each car are normally distributed, with
mean μ = 62 tons and standard deviation σ = 0.9 ton.
(a) What is the probability that one car chosen at random will
have less than 61.5...

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