Answer to Question #138212 in Statistics and Probability for joseph se

Question

1. A survey conducted in Mega Manila with a sample of 350 gasoline stations found that the price charged per liter of gasoline is normally distributed with a mean of P49.50 and a standard deviation of P2.75. Using the empirical rule, determine the number of stations that charge between P46.75 and P52.25.

2. The mean grade in a Physics examination was 73 and the standard deviation was 8. Determine the following: a. The standard scores (z-value) corresponding to a grade of 86. b. The grade of the student whose standard score is –0.8.

Answer 1

1) Using the empirical rule - we can say that in a normal distribution about 68% of data will be within one standard deviation of the mean. 49.50-46.75=2.75=standard deviation;52.25- 49.50=2.75=standard deviation. So we have 350*0.68=238 stations  that charge between P46.75 and P52.25.

2) a) z=(x-mean)/sd, so z(86)=(86-73)/8=1.625

b)z=(x-73)/8=-0.8

x=8*(-0.8)+73=79.4=79