How can i solve this using R? In a road-paving process, asphalt mix is delivered

Question

How can i solve this using R?

In a road-paving process, asphalt mix is delivered to the hopper of the paver by trucks that haul the material from the hatching plant. Suppose the rv X = truck haul time follows a normal distribution with mean value 8.46 min and standard deviation of .913. A. What is the probability that haul time will be at least 10 min? Will exceed 10 min? B. What is the probability that haul time will exceed 15min? c. What is the probability that haul time will be between 8 and 10mins? d. What value c is such that 98% of all haul times are in the interval from 8.46 - c to 8.46+c? e. if four haul times are independently selected, what is the probability that at least one of them exceeds 10mins?

Explanation / Answer

Please see the R code

m <- 8.46
s<- 0.913

#a

z <- (10-m)/s
z

1-pnorm(z)

#b

z <- (15-m)/s
z

pnorm(z)

## 8 and 10 mins

z8 <- (8-m)/s
z8

z10 <- (10-m)/s
z10

pnorm(z10)-(pnorm(z8))

The resutls are

> pnorm(z10)-(pnorm(z8))
[1] 0.6469848
> 1-pnorm(z)
[1] 3.941292e-13
> pnorm(z)
[1] 1
> pnorm(z10)-(pnorm(z8))
[1] 0.6469848

> ## atleast 10 mins
> z <- (9.99-m)/s
> z
[1] 1.675794
>
> 1-pnorm(z)
[1] 0.04688927

Please note that we can answer only 4 subparts of the question at a time

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