New Zealand
Level 7 - NCEA Level 2

# Using z-scores to identify probabilities

## Interactive practice questions

The table below shows the area under the standard normal curve between $0$0 and a given $z$z-score. Use this table to find the probability that a variable has a $z$z-score less than $z=0.85$z=0.85.

Easy
Approx 3 minutes

The average life span of a tortoise is estimated to be approximately $100$100 years, with a standard deviation of $7$7 years.

Use the table below showing the area under the standard normal curve between $0$0 and a given $z$z-score to answer the following questions.

A sprinter is training for a national competition. She runs 400 m in an average time of $75$75 seconds, with a standard deviation of $6$6 seconds.

Use the table below showing the area under the standard normal curve between $0$0 and a given $z$z-score to answer the following questions.

Research scientists have measured the heights of a large number of eucalyptus trees in an area of forest. The average height of these trees is $60$60 m, with a standard deviation of $6$6 m.

Use the table below showing the area under the standard normal curve between $0$0 and a given $z$z-score to answer the following questions.

### Outcomes

#### S7-4

S7-4 Investigate situations that involve elements of chance: A comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions B calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.

#### 91267

Apply probability methods in solving problems