Monthly archive | MATHalino

Find $P(0 \lt z \lt 1.25)$, where $z$ has the standard normal distribution.

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The Design Basis Earthquake (DBE) has a return period of 475 years with 10% probability of exceedance in how many years?

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The length of a telephone conversation is 2.5 minutes on average. What is the probability that a conversation lasts between 3 and 5 minutes?

If queries sent to a search engine arrive every 15 seconds on the average, what is the probability of waiting less than or equal to 30 seconds?

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

The combined ages of Mary and Ann are 44 years.
Mary is twice as old as Ann was when Mary was half
as old as Ann will be when Ann is three times as old as Mary
was when Mary was three times as old as Ann.
How old is Ann?

In square $ABCD$, $E$ is the midpoint of side $\overline{AB}$ and $F$ is a point of side $\overline{AD}$ such that $F$ is twice as near from $D$ as from $A$. $G$ is the intersection of the line segments $\overline{DE}$ and $\overline{CF}$. If $AB = 1\text{ cm}$, find the area of $\triangle CDG$.

There are several ways to solve this problem, please show your solutions.

June 2021

How old is Ann?

Area of a triangle