In: Statistics and Probability
1.A particular fruit's weights are normally distributed, with a
mean of 675 grams and a standard deviation of 5 grams.If you pick
10 fruits at random, then 12% of the time, their mean weight will
be greater than how many grams?
Give your answer to the nearest gram.
2. Karen wants to advertise how many chocolate chips are in each
Big Chip cookie at her bakery. She randomly selects a sample of 60
cookies and finds that the number of chocolate chips per cookie in
the sample has a mean of 7.5 and a standard deviation of 3.5. What
is the 80% confidence interval for the number of chocolate chips
per cookie for Big Chip cookies? Enter your answers accurate to one
decimal place (because the sample statistics are reported accurate
to one decimal place).
? < μ < ?
1. X : Fruits weight
X is normally distributed with mean 675 grams and a standard deviation of 5 grams
Number of fruits picked at random : sample size : n= 10
be their mean weight
Then by central limit theorem, follows normal distribution with mean 675 and standard deviation = 1.5811
Let : mean weight, such that 12% of the time ,
i.e
P() = 0.12
P() = 1-P() = 0.12
P() = 1-0.12 = 0.88
Let Z12 be the z-score for i.e
P(ZZ12) = P() = 0.88
From standard normal tables,
Z12 = 1.175
Z12 = ( - 675)/1.5811
= 1.5811 Z12 +675 = 1.5811 x 1.175 +675 = 676.8578677
If you pick 10 fruits at random, then 12% of the time, their mean weight will be greater than 677 grams
2.
Confidence Interval for Population mean
sample of 60 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 7.5 and a standard deviation of 3.5
n : sample Size : number of cookies in the sample= 60
Sample mean : : 7.5
Sample standard deviation : s = 3.5
Confidence Level : | 80 |
=(100-80)/100 | 0.2 |
/2 | 0.1 |
t0.1,59 | 1.2961 |
80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies
80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies = (6.9, 8.1)
Ans.