MATH 320-MIDTERM QU1Z 03 I. Let X be the GPA of CSUMB students. The population m

Question

MATH 320-MIDTERM QU1Z 03 I. Let X be the GPA of CSUMB students. The population mean of X is = 3 and the population standard deviation is -1. The figure below does not describe the population distribution, but it describes the sampling distribution of the sample mean X when wo take a sample of size -100 Answer the following questions based on the figure a. In the figure, what is the value of c? b. What is the standard error (SE) of the sample mean x? c. In the figure, b and d are the values such that the probability of observing a sample mean between 0.683, if we repeat random sampling of size n 100 infinitely many times. What are the values of b and d? d. In the figure, a and e are the values such that the probability of observing a sample mean between them is 0.954, if we repeat random sampling of size n- 100 infinitely many times. What are the values of a and e? (Hint: Central Limit Theorem) e. If we take a sample of n 100 students, what is the probability that the sample rnean X will be below 2.8

Explanation / Answer

Result:

a). c=3

b). standard error = sd/sqrt(n) = 1/sqrt(100) =0.1

c).

probability of within 1 standard deviation from mean is 0.683

b=meand-1sd = 3-1*0.1 =2.9

d=meand+1sd = 3+1*0.1 =3.1

d).

probability of within 2 standard deviation from mean is 0.954

a=meand-2sd = 3-2*0.1 =2.8

e=meand+2sd = 3+2*0.1 =3.2

e).

z value for 2.8, z =(2.8-3)/0.1 = -2

P( x <2.8) = P( z < -2)

=0.0228

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

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