Question

Refer to speeds at which cars pass through a checkpoint on the highway. Assume the speeds are normally distributed with a population mean of 61 miles per hour and a population standard deviation of 4 miles per hour. Calculate the probability that the next car passing will be travelling more than 58 miles per hour.

Answer #1

Mean = 61 miles per hour

Standard deviation = 4 miles per hour

Value that is being standardized= 58 miles per hour

We need to find the probability

P (Z > (58-61)/4)

or P (Z > -3/4)

or P (Z > -0.75)

P (Z > -0.75) has the same value as P (Z < 0.75). This is because of the symmetry of the standard normal distribution curve.

From standard normal distribution table, P (Z < 0.75) = 0.22663

Thus, P(Z > -0.75) = 0.22663

Hence probability that the next car passing will be travelling more than 58 miles per hour is 0.22663

Assume that the speeds at which all men and all women drive cars
on this highway are both approximately normally distributed with
unknown and unequal population standard deviations. a. Construct a
98% confidence interval for the difference between the mean speeds
of cars driven by all men and all women on this highway. b. Test at
a 1% significance level whether the mean speed of cars driven by
all men drivers on this highway is higher than that of cars...

Suppose that the speeds of cars travelling on California
freeways are normally distributed with a mean of 60 miles/hour. The
highway patrol's policy is to issue tickets for cars with speeds
exceeding 80 miles/hour. The records show that exactly 5% of the
speeds exceed this limit. Find the standard deviation of the speeds
of cars travelling on California freeways. Carry your intermediate
computations to at least four decimal places. Round your answer to
at least one decimal place.

A construction zone on a highway has a posted speed limit of 40
miles per hour. The speeds of vehicles passing through this
construction zone are normally distributed with a mean of 45 miles
per hour and a standard deviation of 5.6 miles per hour. Find the
percentage of vehicles passing through this construction zone that
are exceeding the posted speed limit. Round to four decimal
places.

Suppose the average speeds of passenger trains traveling from
Newark, New Jersey, to Philadelphia, Pennsylvania, are normally
distributed, with a mean average speed of 89 miles per hour and a
standard deviation of 6.4 miles per hour. (a) What is the
probability that a train will average less than 70 miles per hour?
(b) What is the probability that a train will average more than 79
miles per hour? (c) What is the probability that a train will
average between...

Suppose the average speeds of passenger trains traveling from
Newark, New Jersey, to Philadelphia, Pennsylvania, are normally
distributed, with a mean average speed of 85 miles per hour and a
standard deviation of 6.4 miles per hour.
(a) What is the probability that a train will average less than
69 miles per hour?
(b) What is the probability that a train will average more than
81 miles per hour?
(c) What is the probability that a train will average between...

The mean speed of vehicles along a stretch of highway is
56 miles per hour with a standard deviation of 4 miles per
hour. You measure the speeds of three cars traveling
along Route 440 as 62 miles per hour, 47 miles per hour, and 56
miles per hour. Find the Z-score that corresponds to
each speed. What can you conclude?

9. А simple random sample of 40 recorded speeds in miles per
hour is obtained from cars traveling on а section of Highway 405 in
Los Angeles. The sample has а mean of 68.4 miles per hour and а
standard deviation of 5.7 miles per hour. Use а 0.05 significance
level to test the claim that the mean speed of all cars is greater
than the posted speed limit of 65 miles per hour.

A state highway goes through a small town where the posted speed
limit drops down to 40MPH, but which out of town drivers don’t
observe very carefully. Based on historical data, it is known that
passenger car speeds going through the city are normally
distributed with a mean of 47 mph and a standard deviation of 4MPH.
Truck speeds are found to be normally distributed with a mean of
45MPH and a standard deviation of 6MPH. The town installed a...

A highway construction zone has a posted speed limit of 40 miles
per hour. Workers working at the site claim that the mean speed of
the vehicles passing through this constuction zone is at least 50
miles per hour. You think the workers claim is wrong and want to
prove it. A random sample of 36 vehicles passing through this zone
produced a mean speed of 48 miles per hour. The population standard
deviation is known to be 4 miles...

The miles-per-gallon obtained by the 1995 model Z cars is
normally distributed with a mean of 22 miles-per-gallon and a
standard deviation of 5 miles-per-gallon. a. What is the
probability that a car will get between 13.35 and 35.1
miles-per-gallon? b. What is the probability that a car will get
more than 29.6 miles-per-gallon? c. What is the probability that a
car will get less than 21 miles-per-gallon?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 26 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago