A population of values has a normal distribution with = 117.9 and = 17·You inten

Question

A population of values has a normal distribution with = 117.9 and = 17·You intend to draw a random sample of size n = 54 Find the probability that a single randomly selected value is greater than 123.7 P(X> 123.7)- 54 is randomly Find the probability that a sample of size n selected with a mean greater than 123.7 P(M> 123.7)- 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 License Points possible: 6

Explanation / Answer

P(X>123.7)=P[Z>(123.7-117.9)/17] [using formula, Z=(X-xbar)/s, where, xbar is sample mean, s is sample standard deviation, and X is raw score]

=P[Z>0.341] [use Z table to find probability associated with Z score, the table gives area under standard normal curve to the left of Z]

=1-0.6331 [in order to find area greater than a Z score, subtract the area from 1]

=0.3669

According to Central Limit Theorem, for sample size, n=54, the mean, xbar of sampling distribution is xbar=M=117.9, and standard deviation of xbar is sxbar=s/sqrt n=17/sqrt 54=2.313

P(M>123.7)=P[Z>(123.7-117.9)/2.313]=P[Z>2.508]=1-0.9940=0.006

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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