Mathematics, 30.10.2019 04:31 RoyalGurl01

The proportion of traffic fatalities resulting from drivers with high alcohol blood levels in 1982 was approximately normally distributed among u. s. states, with mean 0.569 and standard deviation 0.068 (u. s. department of transportation traffic safety facts 1999). a. what proportion of states would you expect to have more than 65% of their traffic fatali- ties from drunk driving? b. what proportion of deaths due to drunk driving would you expect to be at the 25th percentile of this distribution?

Answers: 1

Show answers

Answers

Using the normal distribution principle, the proportion expected to have more than 65% and number expected to be at the 25% percentile are 0.5428 and 0.5232

Given the Parameters :

Mean, μ = 0.569Standard deviation, σ = 0.068

link

Zscore = (X - μ) ÷ σ

1.) More than 65% of traffic fatalities :

Using a normal distribution table ; Z score for a Pvalue > 0.65 would be : -0.674

Using the Zscore relation :

-0.674 = (X - 0.569) / 0.068

-0.02618 = X - 0.569

X = -0.02618 + 0.569

X = 0.5428

2.) Proportion at the 25 percentile of the distribution :

Using a normal distribution table ; Z score for a Pvalue of 0.25 would be : -0.385

Using the Zscore relation :

-0.385 = (X - 0.569) / 0.068

-0.045832 = X - 0.569

X = -0.02618 + 0.569

X = 0.5232

Therefore, the proportion expected to be at the 25th Percentile is 0.5232.

Learn more :

Answer from: ally0817

a) The proportion of states would you expect to have more than 65% of their traffic fatalities from drunk driving is 0.59518.

b) The 25th percentile of this distribution is a 0.5231 proportion of deaths due to drunk driving.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the percentile of this measure.

In this problem, we have that:

Mean 0.569 and standard deviation 0.068. So $\mu = 0.569, \sigma = 0.068$

a. What proportion of states would you expect to have more than 65% of their traffic fatali- ties from drunk driving?

This is the value of X when Z has a pvalue of 0.65.

Z has a pvalue of 0.65 between Z = 0.38 and Z = 0.39 . So, we use Z = 0.385

$Z = \frac{X - \mu}{\sigma}$

$0.385 = \frac{X - 0.569}{0.068}$

X - 0.569 = 0.068*0.385

X = 0.59518

The proportion of states would you expect to have more than 65% of their traffic fatalities from drunk driving is 0.59518.

b. What proportion of deaths due to drunk driving would you expect to be at the 25th percentile of this distribution?

This is the value of X when Z has a pvalue of 0.25.

Z has a pvalue of 0.65 between Z = -0.67 and Z = -0.68 . So, we use Z = -0.675

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 0.569}{0.068}$

X - 0.569 = 0.068*(-0.675)

X = 0.5231

The 25th percentile of this distribution is a 0.5231 proportion of deaths due to drunk driving.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

if farmer matt works for 8 hours a day, how many days will it take him to completely plant 12 rows of crops? each batch of cookies needs 3/4 cups of sugar.

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:30, hanjonez

Me because some of question i don’t understand

Answers: 1

continue

Mathematics, 21.06.2019 16:30, angelisabeast5430

Sam claims that cos x =sin y if x and y are congruent angels. is sam correct ?

Answers: 2

continue

Mathematics, 21.06.2019 17:40, kayleeemerson77

The graph of h(x)= |x-10| +6 is shown. on which interval is this graph increasing

Answers: 2

continue

Mathematics, 21.06.2019 18:00, ahmedislife

Someone answer this asap rn for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =

Answers: 2

continue

You know the right answer?

The proportion of traffic fatalities resulting from drivers with high alcohol blood levels in 1982 w...