Question

The time taken by a randomly selected student to fill out an online SOTE has a normal distribution with mean 2 minutes and standard deviation 45 seconds. Suppose 4 students fill out an online SOTE on a randomly selected day. Find the probability that the sample average amount of time taken is at most 3 minutes.

Answer #1

Given that,

mean = = 2

standard deviation = = 45 seconds. =0.75 minutes

n = 4

= 2

= / n = 0.75 / 4=0.375

P( < 3) = P[( - ) / < (3-2) /0.375 ]

= P(z <2.67)

Using z table

= 0.9962

probability= 0.9962

The time a student sleeps per night has a distribution with mean
5.98 hours and a standard deviation of 0.35 hours. Find the
probability that average sleeping time for a randomly selected
sample of 50 students is more than 6.05 hours per night.

The time a student sleeps per night has a distribution with mean
6.3 hours and a standard deviation of 0.6 hours. Find the
probability that average sleeping time for a randomly selected
sample of 42 students is more than 6.5 hours per night. Answer:
(round to 4 decimal places)

Suppose that, for a randomly selected high school student who
has taken a college entrance exam, the probability of scoring above
650 is 0.3. A random sample of n = 9 such students was selected.
What is the probability that none of the students scored over
650?

Suppose that the amount of time that students spend studying in
the library in one sitting is normally distributed with mean 46
minutes and standard deviation 19 minutes. A researcher observed 9
students who entered the library to study. Round all answers to 4
decimal places where possible.
What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
If one randomly selected student...

Suppose that the amount of time that students spend studying in
the library in one sitting is normally distributed with mean 43
minutes and standard deviation 23 minutes. A researcher observed 11
students who entered the library to study. Round all answers to 4
decimal places where possible.
What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
If one randomly selected student...

Suppose that the amount of time that students spend studying in
the library in one sitting is normally distributed with mean 49
minutes and standard deviation 19 minutes. A researcher observed 14
students who entered the library to study. Round all answers to 4
decimal places where possible. What is the distribution of X X ? X
X ~ N(,) What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) What is
the distribution of ∑...

Suppose the random variable X records a randomly selected
student’s score on a national test, where the population
distribution for the score is normal with mean 70 and standard
deviation 5. A simple random sample of 200 students is taken.
(a) What is the distribution of the sample mean score? Is this
the exact distribution or an approximated distribution?
(b) What is the probability that the sample mean will exceed
71?
(c) What is the probability that the sample mean...

The length of time it takes college students to find a parking
spot in the library parking lot follows a normal distribution with
a mean of 6.5 minutes and a standard deviation of 1 minute.
a. Find the probability that it will take a randomly selected
college student more than 4.0 minutes to find a parking spot in the
library parking lot.
b. Find the probability that a randomly selected college student
will find a parking spot in the library...

For a school, the principal expected that a student takes 45
minutes to travel to school on average. Suppose the time taken to
travel to school by a student follows a normal distribution. 100
students are randomly selected from the school for interview and
they took on average 44 minutes to travel to school with a standard
deviation of 15 minutes. 6 of the selected students had lateness
record in the last month.
Construct a 95% confidence interval for the...

A survey was taken of 383 students that asked the question how
much time they spent watching television in a day (in minutes).
Suppose this sample study follows a Normal distribution with a
sample mean x-bar = 118 minutes. Also suppose the population has a
standard deviation σ = 53 minutes. Determine a 96% confidence
interval for the mean television watching time.
A. 112.67 to 123.31
B. 117.86 to 118.14
C. 112.44 to 123.56
D. 111.70 to 124.30

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 18 minutes ago

asked 36 minutes ago

asked 38 minutes ago

asked 38 minutes ago

asked 39 minutes ago

asked 49 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago