1. A particular fruit's weights are normally distributed, with a mean of 416 grams and a standard deviation of 6 grams.
If you pick 8 fruits at random, then 2% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

2. Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.8 grams and a standard deviation of 1.89 grams. ___

a) For samples of size 16 pizza slices, what is the standard deviation for the sampling distribution of the sample mean? ___

b) What is the probability of finding a random slice of pizza with a mass of less than 67.4 grams? ___

c) What is the probability of finding a 16 random slices of pizza with a mean mass of less than 67.4 grams? ___

d) What sample mean (for a sample of size 16) would represent the bottom 15% (the 15th percentile)? ___ grams

probability for j is 1/4

while

a is 1/6

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

what

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4