Question

In: Statistics and Probability

The average modulus of rupture (MOR) for a particular grade of pencil lead is known to...

The average modulus of rupture (MOR) for a particular grade of pencil lead is known to be 6500 psi with a standard deviation of 250 psi.

a) Find the probability that a random sample of 16 pencil leads with have an average MOR between 6400 and 6550 psi.

Expert Solution

Solution :

Given that,

mean = = 6500

standard deviation = = 250

n = 16

= = 6500

= / n = 250 / 16 = 62.5

P(6400< < 6550)

= P[(6400 -6500) /62.5 < ( - ) / < (6550 -6500) /62.5 )]

= P(-1.60 < Z < 0.80)

= P(Z < 0.80 ) - P(Z < -1.60 )

Using standard normal table

= 0.7881 - 0.0548 = 0.7333

Probability = 0.7333

orchestra answered 1 year ago

In a particular country, it is known that college students report falling in love an average...

In a particular country, it is known that college students report falling in love an average of 2.20 times during their college years. A sample of five college students originally from that country but who have spent their entire college career in Canada, were asked how many times they had fallen in love during their college years. Their numbers were 2, 3, 5, 5, and 2. Using the .05 significance level, do exchange students like these who go to college...

The refills for a particular mechanical pencil are supposed to be 0.5 mm in diameter. A...

The refills for a particular mechanical pencil are supposed to be 0.5 mm in diameter. A firm makes refills with diameters whose differences from the correct size are normally distributed with mean 0.5 mm and standard deviation 0.01 a. Suppose you took a sample of 50 pencils. According to the Central Limit Theorem, how would the sample mean of refill thickness vary from sample to sample? b. Refills below 0.485 mm do not stay in the pencil, while refills above...

What is the best mechanical pencil lead size (i.e. 0.5, 0.7 etc) and lead type (I.e....

What is the best mechanical pencil lead size (i.e. 0.5, 0.7 etc) and lead type (I.e. Hb etc) for engineering drawing (isometric and orthogonal) ?

The flow limit of commercial-grade aluminum is given as σ = 120 MPa, the modulus of...

The flow limit of commercial-grade aluminum is given as σ = 120 MPa, the modulus of elasticity is E = 70 GPa and the density is 2.7 gr / cm3. a) There is a 4mm diameter and 3m long wire which made with this material. How many N should be applied to make this wire 3mm longer? b) If a 4 mm diameter wire made of this material is hung from the ceiling, what should be the total length of...

Twelve samples of water from a particular source have an average lead concentration of 12.5μg/L with...

Twelve samples of water from a particular source have an average lead concentration of 12.5μg/L with a standard deviation of 2.0μg/L. The 95% confidence interval for the lead concentration in water from this source is approximately

What properties do you use to determine the grade of steel (ie modulus of elasticity)?

What do you think would happen if you connected the pencil lead connected to the negative...

What do you think would happen if you connected the pencil lead connected to the negative post after being in the copper nitrate solution to the positive post of the battery? explain why you think there would or would not be an observable change.

In a factory, it is known that the probability of fixing a particular production error is...

In a factory, it is known that the probability of fixing a particular production error is 1/3. For production of 10 units with this error; a-)Write the probability function. b-)What is the probability that all three can be corrected? c-)What is the probability that one of the most errors can be fixed? d-)What is the probability that two or more errors can be corrected? e-)What is the probability that more than three, 5 or fewer errors can be corrected?

A particular human hair has a Young's modulus of 3.77×109 N/m2and a diameter of 146 μm....

A particular human hair has a Young's modulus of 3.77×109 N/m2and a diameter of 146 μm. If a 256 g object is suspended by the single strand of hair that is originally 15.5 cmlong, by how much ΔL hair will the hair stretch? If the same object were hung from an aluminum wire of the same dimensions as the hair, by how much ΔLAl would the aluminum stretch? If the strand of hair is modeled as a spring, what is...

Suppose that the probability of obtaining a particular grade in an undergraduate statistics course, is defined...

Suppose that the probability of obtaining a particular grade in an undergraduate statistics course, is defined by the following table: grade A B C D F probability .25 .35 .2 .15 .05 (a) Using the usual numerical values for the grades, define the corresponding random variable, X, and its probability mass function, p(x). (b) Calculate P(X ≤ 2), P(X < 2), and P(X ≥ 3). (c) Plot the cumulative distribution function F(x). (d) Compute the mean µ = E(X).