Answer to Question #308555 in Statistics and Probability for Secret Person

Question

The average time it takes for a high school students to complete certain examination is 46.2 minutes. The standard deviation is 8 minutes. There will be 50 random samples to be selected. Assume that the variable is normally distributed.

1. What is the population mean in the given problem?

a. 0

b. 8

c. 46.2

d. 50

2. What is the value of n in the given problem?

a. 0

b. 8

c. 46.2

d. 50

3. If 50 random selected high school students take the exam, what is the probability that the mean time it takes the group to complete the test will be less than 43 minutes?

a. 0.23%

b. 2.3%

c. 3%

d. 23%

Answer 1

1. The population mean is the average time, so it is equal to 46.2(c)
2. n is sample size, so n = 50(d)
3. Let X be a random variable repreenting the mean time of completing examination for 50 people, then, according to the central limit theorem, X ~ $N(46.2,{\frac {8^2} {50}})=N(46.2, 1.28)$

$P(X<43)=P(N(46.2,1.28)<43)=P(46.2+1.13N(0,1)<43)=P(N(0,1)<-2.83)=0.00233$

So, the answer is 0.23%(a)