Question

The average grade/mark of all college students is 70 with standard deviation of 20. If a random sample of 49 students is taken, what is the probability that the sample average grade/mark is
a) At least 65
b) Less than 78
c) Between 65 and 72

Answer 1

$P(65\le)$

$Z=\frac{65-70}{\frac{20}{7}}=-1.75$

$P(65\le)= 1-P(Z\le-1.75)$

From z table, we have $1-0.040059=0.959941$

$P(78\ge)$

$Z=\frac{78-70}{\frac{20}{7}}=2.8$

$P(78\ge)= P(Z\le2.8)$

From z table, we have 0.997445

$P(65\le x\le72)$

$Z=\frac{72-70}{\frac{20}{7}}=0.7$

$P(65\le x\le72)=P(-1.75\le Z\le0.7)$

From z tables we have $0.758036-0.040059=0.717977$