Question

A final exam in Math 160 has a mean of 73 with a standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 70.

A: 0.1006
B: 0.0278
C: 0.9699
D: 0.0301

Answer 1

z(70)=(70-73)/7.8/sqrt(24)=-1.88442228...

P(z<-1.88442228...)=0.02975...

Explanation:

Answer 2

Answer: Option 'D' is correct.

Explanation:

Since we have given that

Mean = 73

Standard deviation = 7.8

Number of students are randomly selected = 24

So, n = 24.

Since it is normally distributed , so, we have

[tex]P(x<70)=P(z<\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}})=P(z<\frac{70-73}{\frac{7.8}{\sqrt{24}}}\\\\P(z<\frac{-3}{1.592})\\\\=P(z<-1.88)\\\\=0.03005=0.0301/tex]

Hence, Option 'D' is correct.