Statistics question. Samples from a particular lot of soil have a true mean and

Question

Statistics question.

  Samples from a particular lot of soil have a true mean and standard deviation of iron content of 5 grams and 1 gram, respectively. Students in GEO 101 where given one sample each and had to determine the iron content.

a. For ten students, what is the probability that their sample mean iron content is between 4.9 and 5.1 grams?

b. For forty students, what is the probability that their sample mean iron content is less than 5.01 grams?

I attempted to solve part A by finding the sample deviation then taking the true deviation over sample deviation and finding the z values of those probabilities. Anyways I don't think I did it correctly as my probability was very vey small. Can you please show what formulas are used, what nomenclature/terminology and the process.

Thanks!!

Explanation / Answer

Statistics question.

  Samples from a particular lot of soil have a true mean and standard deviation of iron content of 5 grams and 1 gram, respectively. Students in GEO 101 where given one sample each and had to determine the iron content.

Standard error =sd/sqrt(n)=1/sqrt(10) =0.3162

Z value for 4.9, z=(4.9-5)/0.3162 =-0.32

Z value for 5.1, z=(5.1-5)/0.3162 =0.32

P( 4.9<x<5.1) =P( -0.32 <z<0.32)

P( z <0.32) – P( z <-0.32)

= 0.6255 - 0.3745

=0.251

b. For forty students, what is the probability that their sample mean iron content is less than 5.01 grams?

Standard error =sd/sqrt(n)=1/sqrt(40) =0.1581

Z value for 5.01, z=(5.01-5)/0.1581 = 0.06

P( x <5.01) =P( z <0.06) = 0.5239

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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