# Data Driven Statistics

**Question description**

1. 75% of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Find the probability that the numbers that say they would feel secure is (a) exactly five, (b) more than 5, and (c) at most five.

Exactly 5___

More than 5___

At most 5___

**(ROUND
TO THREE DECIMAL PLACES AS NEEDED)**

2. 22% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. If convenient, use technology to find the probabilities.

**(ROUND
TO THE NEAREST THOUSANDTH AS NEEDED)**

3. 5% of the people in a city eligible to donate blood actually do. You randomly select four eligible blood donors and ask them if they donate blood.

Construct a binomial distribution for n = 4
and p = 0.05 (**Round to three decimal
places as needed.)**

**X P(x)**

0 ___

1 ___

2 ___

3 ___

4 ___

4. Find the area of the shaded region. The graph depicts the standard normal distribution with mean0 and standard deviation 1.

(On the graph that is not shown is z= 0.84 which is shaded)

**(ROUND
TO THE FOUR DECIMAL PLACES AS NEEDED)**

The area of the shaded region is ___

5. Find the indicated area under the standard normal curve. To the right of z = 0.74.

The area to the right of z= 0.74 under the standard normal curve is___

**(ROUND
TO FOUR DECIMAL PLACES AS NEEDED)**

**6. **For
the standard normal distribution find the probability of z

Z= 1.39

The probability is ___

**(ROUND
TO FOUR DECIMAL PLACES AS NEEDED)**

7. Find the indicated probability using the standard normal distribution.

P(x>0.87)___ **(ROUND
TO FOUR DECIMAL PLACES AS NEEDED**)

8. Find the indicated probability using the standard normal distribution.

P (-1.27<z<1.27)=___(**ROUND TO FOUR DECIMAL PLACES AS NEDED)**

9. A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age groups, the heights were normally distributed, with a mean of 68.3 inches and standard deviation of 3.0 inches. A study participant is randomly selected.

Find the probability that is less than 65 inches.

The probability that the study participant selected at random is less than 65 inches tall is ___

**(ROUND TO FOUR DECIMAL PLACES AS NEEDED)**

**10. **Use
the normal distribution of fish lengths for which the mean is 10 inches and the
standard deviation is 2 inches. Assume
the variable x is normally distributed.

(a) What percent of the fish are longer than 11 inches?

(b) If 300 fish are randomly selected, about how many would you expect to be shorter than 7 inches?

**(ROUND TO TWO DECIMAL PLACES AS
NEEDED)**

**11. **Use
the standard normal table to find the z-score that corresponds to the
cumulative area 0.0090. If the area is
not in the table, use the entry closest to the area. If the area is halfway between two entries,
use the z-score halfway between the corresponding z-scores.

Z= ____

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