Please help with questions D and E.Thanks 1. Federal law under Title 49 of the United States Code, Chapter 301, Motor Vehicle SafetyStandard took effect on January 1, 1968 and required all vehicles (except buses) to be fittedwith seat belts in all designated seating positions. While most states have laws requiring seatbelt use today, some people still do not “buckle up." Let's assume that 90 % of drivers do"buckle up." If drivers are randomly stopped to check seat belt usage, answer the followingquestions and show your work.a) How many drivers do they expect to stop before finding a driver whose seatbelt is notbuckled?b) What is the probability that the second unbelted driver is in the ninth car stopped?c) What is the probability that of the first 10 drivers, 8 or more are wearing their seatbelts?d) If they stop 30 cars during the first hour, find the mean and standard deviation of thenumber of drivers not expected to be wearing seatbelts?e) If they stop 120 cars during this safety check, what is the probability they find at least 12drivers not wearing seatbelts?

Name: Please help with questions D and E.Thanks 1. Federal law under Title 4
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please help with questions D and E.Thanks 1. Federal law under Title 49 of the United States Code, Chapter 301, Motor Vehicle SafetyStandard took effect on January 1, 1968 and required all vehicles (except buses) to be fittedwith seat belts in all de

Answered: d) If they stop 30 cars during the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

Please help with questions D and E.

Thanks

1. Federal law under Title 49 of the United States Code, Chapter 301, Motor Vehicle Safety
Standard took effect on January 1, 1968 and required all vehicles (except buses) to be fitted
with seat belts in all designated seating positions. While most states have laws requiring seat
belt use today, some people still do not “buckle up." Let's assume that 90 % of drivers do
"buckle up." If drivers are randomly stopped to check seat belt usage, answer the following
questions and show your work.
a) How many drivers do they expect to stop before finding a driver whose seatbelt is not
buckled?
b) What is the probability that the second unbelted driver is in the ninth car stopped?
c) What is the probability that of the first 10 drivers, 8 or more are wearing their seatbelts?
d) If they stop 30 cars during the first hour, find the mean and standard deviation of the
number of drivers not expected to be wearing seatbelts?
e) If they stop 120 cars during this safety check, what is the probability they find at least 12
drivers not wearing seatbelts?

Expert Solution

Step 1

Given Information:

90% of drivers do "buckle up" (wearing seat belts).

(d) If they stop 30 cars during the first hour, we are asked to find the mean and standard deviation of the number of drivers not expected to be wearing seatbelts:

If $P (d r i v e r s w e a r i n g s e a t b e l t s) = 0.90$ , then $P (n o t w e a r i n g s e a t b e l t s) = 1 - 0.90 = 0.10$

Let X be a Binomial random variable with parameters $n = 30$ and $p = 0.10$

Mean or Expected value of Binomial variable is given as:

$\begin{array}{rcl} E (X) & = & μ = n p \\ = & 30 (0.10) \\ = & 3 \end{array}$

Thus, the mean of the number of drivers not expected to be wearing seatbelts is 3

Standard deviation is calculated using the formula:

$\begin{array}{rcl} σ & = & \sqrt{n p (1 - p)} \\ = & \sqrt{30 (0.10) (1 - 0.10)} \\ = & \sqrt{2.7} \\ = & 1.643167673 \end{array}$

Thus, the standard deviation of the number of drivers not expected to be wearing seatbelts is 1.6432

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Research Design Formulation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions