A set of final examination grades in an introductory statistics course is normal

Question

A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 72 and a standard deviation of 8. Complete parts (a) through (d). What is the probability that a student scored below 86 on this exam? The probability that a student scored below 86 is 0.9599. (Round to four decimal places as needed.) What is the probability that a student scored between 64 and 95? The probability that a student scored between 64 and 95 is 0.8393. (Round to four decimal places as needed.) The probability is 5% that a student taking the test scores higher than what grade? The probability is 5% that a student taking the test scores higher than (Round to the nearest integer as needed.)

Explanation / Answer

P (X<86)=0.9599

Explanation

Since =72 and =8 we have:

P ( X<86 )=P ( X<8672 )=P (X/<8672/8)

Since x/=Z and 8672/8=1.75 we have:

P (X<86)=P (Z<1.75)

Use the standard normal table to conclude that:

P (Z<1.75)=0.959

P (64<X<95)=0.8393

Explanation

Since =72 and =8 we have:

P ( 64<X<95 )=P ( 6472< X<9572 )=P ( 6472)/8<X/<9572/8)

Since Z=x/ , 6472/8=1 and 9572/8=2.88 we have:

: Use the standard normal table to conclude that:

P ( 1<Z<2.88 )=0.8393

Case 3:

The probability is 5% that a student has test scores higher than 85.

Kindly Upvote if Helpful :)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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