Posted by Steven on Monday, December 16, 2013 at 12:53pm.
A manufacturing facility produces iron rods whose mean diameter is 2.5 inches with a standard deviation of 0.2 inch. If a sample of 50 metal rods produced by the facility were randomly selected, what is the probability that the mean of these rods will lie between 2.4 inches and 2.8 inches?
According to census statistics, Hispanics comprise 27.5% of the population of New York City. Suppose a random sample of 400 people is selected from New York City. What is the probability that there are fewer than 22% of Hispanics in the sample? Hint: Use Normal approximation to the Binomial distribution.
- Statistics - MathGuru, Monday, December 16, 2013 at 6:46pm
z = (x - mean)/(sd/√n)
Find two z-scores:
z = (2.4 - 2.5)/(0.2/√50) = ?
z = (2.8 - 2.5)/(0.2/√50) = ?
Finish the calculations.
Next, check a z-table to find the probability between the two scores.
Find mean and standard deviation.
mean = np = 400 * .275 = ?
standard deviation = √npq = √(400 * .275 * .725) = ?
Note: q = 1 - p
Finish the calculations.
Next, use z-scores:
z = (x - mean)/sd
z = (.22 - mean)/sd
Substitute the mean and standard deviation into the z-score formula and calculate, then use a z-table to find the probability.
I hope this will help get you started.
- Statistics - MathGuru, Monday, December 16, 2013 at 6:48pm
Note: For the second problem, we use the normal approximation to the binomial distribution when finding the mean and standard deviation.
- Statistics - Steven , Tuesday, December 17, 2013 at 7:09pm
How would you check the Z table for the first problem?
Answer this Question
More Related Questions
- statistics - A company produces steel rods. The lengths of the steel rods are ...
- PHYSICS - Two parallel METAL rods form a plane inclined at 20.0° to the ...
- Statistics - The inside diameter of the automobile wheel bearing sets at a ...
- statistics - The diameter of small Nerf balls manufactured at a factory in China...
- Elementary Statistics - The diameters of pencils produced by a certain machine ...
- Statistics - Tennis Ball Manufacturing: A company manufactures tennis balls. ...
- statistics - The heights of South African men are normally distributed with a ...
- statistics - Heights of fences are normally distributed with a mean of 52 inches...
- statistics - in certain manufacturing processes parts must be machined tonwithin...
- Statistics: Sample Size, Variance and Standard Dev - Sample Size, Variance and ...