What is a z-score?

Tags

CCSS.HSS.ID.A.4

If I tell you that you scored at the 55th percentile on your final exam, you would know:

• 55% of the class scored the same or worse than you did

• You earned a 55% on the exam

• You failed the exam

• 45% of the class scored worse than you did

• 55% of the class scored the same or better than you did

Tags

CCSS.HSS.IC.A.1

Suppose a data set is represented by a normal distribution with a mean of 10 and a standard deviation of 2.

What is z-score for a data value of 17?

Mathematical Equivalence

ON

Between what two standard deviations of a normal distribution contain 68% of the data?

• -1 and 1

• -2 and 2

• -2 and 0

• 0 and 2

Tags

CCSS.HSS.ID.A.4

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds.  What is the z-score for a player who runs a time of 5.6 seconds?

Round to the hundredths place.

Mathematical Equivalence

ON

Tags

CCSS.HSS.ID.A.4

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have less than 5 accidents?

Answer this question using the standard normal table. Show your work.

Mathematical Equivalence

ON

The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and 𝞂 = 15.

Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?

Mathematical Equivalence

ON

Tags

CCSS.HSS.ID.A.4

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 75th percentile.  How long was his jump?

Mathematical Equivalence

ON

Tags

CCSS.HSS.ID.A.4

In 2017 the SAT scores in Virginia were approximately normally distributed with a mean of 1102 and a standard deviation of 184. You may use any method to answer the question, but you must show your work for your chosen strategy:

What proportion/percentage of scores fall between 1000 and 1200?

In 2017 the SAT scores in Virginia were approximately normally distributed with a mean of 1102 and a standard deviation of 184. You may use any method to answer the question, but you must show your work for your chosen strategy:

What SAT score marks the 60th percentile? Round to the nearest hundredth.