Enter your answers as numbers accurate to 4 decimal places. Answers obtained usi

Question

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

b.) A population of values has a normal distribution with =31.1 and =51.6. You intend to draw a random sample of size n = 147.

Find the probability that a single randomly selected value is less than 38.8. P(X < 38.8) =

Find the probability that a sample of size n = 147 is randomly selected with a mean less than 38.8. P(M < 38.8) =

c.) A population of values has a normal distribution with =201.1 and =93. You intend to draw a random sample of size n=189.

Find P47, which is the score separating the bottom 47% scores from the top 53% scores.
P47 (for single values) =

Find P47, which is the mean separating the bottom 47% means from the top 53% means.
P47 (for sample means) =

e.) A population of values has a normal distribution with =79 and =17.8. You intend to draw a random sample of size n=12.

Find the probability that a sample of size n=12n=12 is randomly selected with a mean between 65.1 and 66.2.
P(65.1 < M < 66.2) =

f.) A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 255.1-cm and a standard deviation of 1.1-cm. For shipment, 14 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 255-cm.
P(M > 255-cm) =

Explanation / Answer

b) probability that a single randomly selected value is less than 38.8. P(X < 38.8)

=P(Z<(38.8-31.1)/51.6)=P(Z<0.1492)=0.5593

std error of mean =std deviation/(n)1/2 =4.256

Find the probability that a sample of size n = 147 is randomly selected with a mean less than 38.8. P(M < 38.8)

=P(Z<(38.8-31.1)/4.256)=P(Z<1.8093)=0.9648

c)here std error of mean =std deviation/(n)1/2 =6.7648

for 47 percentile z=-0.0753

score separating the bottom 47% scores from the top 53% scores.
P47 (for single values) = mean + z*std deviation =194.0999

Find P47, which is the mean separating the bottom 47% means from the top 53% means.
P47 (for sample means) = mean + z*std errror =200.5908

e)std error of mean =std deviation/(n)1/2 =5.1384

P(65.1<M<66.2)=P((65.1-79)/5.1384<Z<(66.2-79)/5.1384)=P(-2.7051<Z<-2.4910)=0.0064-0.0034=0.0030

f)std error of mean =std deviation/(n)1/2 =0.294

P(M>255)=1-P(M<255)=1-P(Z<(255-255.1)/0.294)=1-P(Z<-0.3402)=0.3669

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.