Question

A data set lists weights​ (lb) of plastic discarded by households. The highest weight is

5.265.26

​lb, the mean of all of the weights is

x overbarxequals=2.2092.209

​lb, and the standard deviation of the weights is

sequals=1.1011.101

lb.a. What is the difference between the weight of

5.265.26

lb and the mean of the​ weights?

b. How many standard deviations is that​ [the difference found in part​ (a)]?

c. Convert the weight of

5.265.26

lb to a z score.d. If we consider data speeds that convert to z scores between

minus−2

and 2 to be neither significantly low nor significantly​ high, is the weight of

5.265.26

lb​ significant?

a. The difference is

nothing

lb.

​(Type an integer or a decimal. Do not​ round.)

b. The difference is

nothing

standard deviations.

​(Round to two decimal places as​ needed.)

c. The z score is

zequals=nothing.

​(Round to two decimal places as​ needed.)

d. The highest weight is

Answer 1

(a) The difference between the highest weight and mean weight is 3.051 lb.

(b) The number of standard deviations is 2.77.

(c) The z-score of 5.26 is 2.77.

(d) The weight of 5.26 lb is significantly​ high.

Explanation:

The random variable X is defined as the weights​ (lb) of plastic discarded by households.

The highest weight is,
`X_(max.)=5.26\ lb`

The mean weight is,
`\bar x=2.209\ lb`.

The standard deviation of the weight is,
`s=1.101\ lb`.

(a)

Compute the difference between the highest weight and mean weight as follows:

`X_(max.)-\bar x=5.26-2.209=3.051`

Thus, the difference between the highest weight and mean weight is 3.051 lb.

(b)

Compute the number of standard deviations the mean is from the maximum value as follows:

`Number\ of\ standard deviation=(X_(max.)-\bar x)/(s)=(3.051)/(1.0101)=2.77`

Thus, the number of standard deviations is 2.77.

(c)

The formula of z-score is:

`z=(X-\bar x)/(s)`

Compute the z-score for X = 5.26 as follows:

`z=(X-\bar x)/(s)=(5.26-2.209)/(1.101)=2.77`

Thus, the z-score of 5.26 is 2.77.

(d)

The z-scores between -2 and 2 are considered as neither significantly low nor significantly​ high.

The z-score for X = 5.26 is 2.77.

The value of z > 2.

Thus, the weight of 5.26 lb is significantly​ high.