Question

1) A particular fruit's weights are normally distributed, with a mean of 678 grams and a standard deviation of 28 grams. If you pick 3 fruits at random, then 6% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

2)A population of values has a normal distribution with μ=190.6 and σ=4.4. You intend to draw a random sample of size n=147.

Find P₇₅, which is the score separating the bottom 75% scores from the top 25% scores.
P₇₅ (for single values) =

Find P₇₅, which is the mean separating the bottom 75% means from the top 25% means.
P₇₅ (for sample means) =

Answer 1

1)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	678
std deviation   =σ=	28.000
sample size       =n=	3
std error=σx̅=σ/√n=	16.16581

for 3th percentile critical value of z=		-1.881
therefore corresponding value=mean+z*std deviation=			647.5955~ 648 gram

2) (for single values)

for 75th percentile critical value of z=		0.674
therefore corresponding value=mean+z*std deviation=			193.5678~ 193.6

(for sample means) :

std error=σx̅=σ/√n=

0.3629

therefore corresponding value=mean+z*std deviation=

190.8448~ 190.8