TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Levajkovic)/Übungen 2023W/HW04.3

Acryic nails

One of the most popular types of artificial nails are acrylic nails. These full nail extensions are made from a combination of liquid monomer and powder polymer. Given that 10% of the acrylic nails made using a certain manufacturing process have a length less than 5.8 centimeters, while 5% have a length greater than 6.7 centimeters, what are the mean and the standard

deviation of the lengths of the nails? Assume that the lengths have a normal distribution.

Dieses Beispiel ist als solved markiert. Ist dies falsch oder ungenau? Aktualisiere den Lösungsstatus (Details: Vorlage:Beispiel)

Lösungsvorschlag von Lessi

--Lessi 2024-02-07T13:04:11Z

# we want to get the mean and stdev based on P(X <= 5.8) = 0.1 and P(X >= 6.7) = 0.05 (which means P(X <= 6.7) = 0.95)

# we can use standardization to get mu and sigma, but first we need to compute the 0.1 and 0.95 quantile 
z = c(qnorm(0.1), qnorm(0.95))
print(z)

# now after we formed a equation system based on the standardization we solve for mu and sigma

coeffs <- matrix(c(1, 1, z), nrow=2, ncol=2)
print(coeffs)

vals <- matrix(c(5.8, 6.7), nrow = 2, ncol=1)
print(vals)

solve(coeffs, vals)