Question

The average price of a college math textbook is $166 and the standard deviation is $26. Suppose that 17 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.

1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
2. For the group of 17, find the probability that the average price is between $164 and $167.
3. Find the first quartile for the average textbook price for this sample size. $ (round to the nearest cent)
4. For part b), is the assumption that the distribution is normal necessary? YesNo

Answer 1

Let X be the price of college math textbook

X~ Normal (166, 26)

n= 17

a) ~ Normal ( 166,   )

b) P( 164 < < 167) = P( < < )

= P( -0.32 < z < 0.16)

= P( z < 0.16) - P(z < -0.32)

= P(z < 0.16) - 1 + P( z < 0.32)

= 0.56356 - 1 +0.62552

= 0.18908

c) Firt quartile means , we need to find thw 25th percentile

P( Z < z) =0.25

P( Z < -0.674 ) =0.25

z = -0.674

   = -0.674

= -0.674

= 161.75

So , the first quartile for the average textbook price for this sample size is $161.75

d) Yes the assumtion of the normal distribution is necessary as the sample size is small.