normal distribution question with percentages

Question

how a can i solve a normal distribution without the mean ? suppose a truck of river sand delivered by a company has normal distribution with a standard deviationof 100kg.if 20% of loads are at least 22 tonnes what is the probability that we get at least 20 tonnes of sand froma delivery?

Answer 1

Hints:

• For a standard normal distribution with mean $0$ and standard deviation $1$, at what value is $20\%$ of the distribution above that value.
• How many standard deviations above the mean does that represent?
• If the standard deviation were $0.1$ then how far below $22$ would the mean be?
• What is the probability of at least $20$ given that calculated mean and a standard deviation of $0.1$?

Answer 2

Find the $z$ value of a normal distribution with stdev=100 at $0.2$.

$z_{0.2}*100kg + \mu = 22$

... that gives you $\mu$.

$z_{x}*100kg + \mu = 20$

... find $x$ to solve.