Question

Students of a large university spend an average of $7 a day on lunch. The standard deviation of the expenditure is $2. A simple random sample of 25 students is taken.

1. What is the probability that the sample mean will be at least $4?
2. Jason spent $15 on his lunch. Explain, in terms of standard deviation, why his expenditure is not usual.
3. Explain what information is given on a z table. For example, if a student calculated a z value of 2.77, what is the four-digit number on the z table that corresponds with that value? What exactly is that 4-digit number telling us?
4. Explain why we use z formulas. Why don't we just leave the data alone? Why do we convert?

Answer 1

Answer)

Mean = $7

S.d = $2

N = 25

1)

P(x>4)

First we need to find the z score

Z = (x-mean)/(s.d/√n)

Z = −7.5

From z table, p(z>-7.5) = 1

2)

Anything above 3 standard deviation or below 3 standard deviation is not usual

Here s.d = 2

Mean = 7

7 + 2*3 = 13

15 is above 3 standard deviation, so it is not usual.

3)

From z table

P(z<2.77) = 0.9972

It means that below the z score of 2.77, 99.72% of the data lies.

4)

Formula for z is

Z = (x-mean)/s.d

So, x = z*s.d + mean

So, z score tells us how much standard deviation away our score is from the mean.

And thats what the z table shows us, the probability the score is y standard deviation away from the mean.