Free Printable SIT Week 5: Z-Scores

1.

The heights of women at TWU is approximately normal with a mean $\mu=60$ inches and standard deviation $\sigma=2$ inches. What is the probability that a randomly selected woman is 64 inches or shorter?

(a)

2.

What equation do you use to find z-score?

a)

$z=\frac{\sigma-\mu}{x}$

b)

$z=\frac{\mu-x}{\sigma}$

c)

$z=\frac{x-\mu}{\sigma}$

d)

$z=\frac{x+\mu}{\sigma}$

3.

The weights of corgi's have a normal distribution with a mean $\mu=22.4$ pounds and standard deviation $\sigma=2.0$ pounds. What is the probability that a randomly selected corgi weighs more than 27 pounds?

(a)

4.

The amount of tips waiters makes is approximately normal with a mean $\mu=88$

and standard deviation $\sigma=8$ . What is the probability that a randomly selected waiter makes between $64 and $90 in tips?

(a)

5.

Which curve represents the $75^{th}$ percentile?

a)

b)

c)

6.

Grades on the elementary statistics final at TWU are normally distributed, with

μ=74 and σ=5.

Billy scored a 71 on the final and Susan scored a 77.

Who did relatively better on the final?

a)

Billy

b)

Susan

c)

both did relatively better

d)

neither did relatively better

7.

A random variable X is normally distributed $\mu=12.0$ and $\sigma=2$ .

Find the P(X=8.0).

a)

0.0228

b)

0.9772

c)

0

d)

not enough information given

8.

Assume that bags of Cheetos are filled so that the actual amounts have a mean $\mu=6.2\ oz$ and a standard deviation $\sigma=2.8\ oz$ . Find the probability that a randomly selected bag of Cheetos has a mean amount no more than 4.8 oz.

a)

0.6915

b)

0.3085

c)

0.0456

d)

none of the above

9.

Select all of the properties of a Standard Normal Distribution:

a)

the graph is symmetric and bell-shaped

b)

the total area under the curve is 1

c)

the unit for z-scores is whatever is given in the problem (ex: ounces, inches, grams...)

d)

the mean is 0 with a standard deviation of 1

e)

the mean, median, and mode are centered in the middle

10.

Find one of the z-scores that separate the middle 90% of the data. (answer can be positive or negative)

(a)

SIT Week 5: Z-Scores

Total questions: 10

Worksheet time: 3hrs 30mins

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