library(ggplot2)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
x<-qnorm(0.9, mean=70, sd=10)

Answer

Students will have to score at least 83 points in order to score an A on the test. The calculations were made as the following:

  1. I used the function “qnorm” since I wanted to find the value of x that was placed in a certain range rather than the percentage.

  2. I then wrote “0.9” in order to find the value of x when its probability is 90%, as the values above x will then represent the top 10%.

  3. I then inserted the values of the mean and the standard deviation of the data accordingly.

sample_mean<-35
sample_std_dev<-5
sample_size<-10
percentage<-95

t_value<-qt(percentage/100,df=sample_size-1,sample_mean, sample_std_dev)
print(t_value)
## [1] 57.6914

Answer

The least weight of the milk has to be approximately 58kg. The calculation was conducted as the following:

  1. I assigned the mean, standard deviation, sample size, and the percentage accordingly.

  2. I used the “qt” function as I wanted to find the value that was on 95%.

  3. I subtracted 1 from the sample size to indicate the degrees of freedom.

  4. The final answer was 57.6914.

sample_mean <- 35
sample_std_dev <- 5
threshold <-40
sample_size <-10

t_value <- (threshold - sample_mean) / (sample_std_dev / sqrt(sample_size))
answer <- 1 - pt(t_value, df = sample_size - 1)
answer * 100
## [1] 0.5753993

Answer

Farms with the average of 40kg of milk is 58% of the whole. The calculation was conducted as teh following:

  1. I assigned the mean, standard deviation, sample size, and the threshold accordingly.

  2. I found the t_value by using the equation.

  3. I subtracted pt(t_value, df=sample_size-1) from 1 to find the probability of the x value being HIGHER than the threshold.