Statistics and Probability Answers

The IOs of 600 applicants to a certain college are approximately normally distributed with a mean of 115 and a standard deviation of 12. If the college requires an IQ of at least 95, how many of these students will be rejected on this basis, regardless of their qualifications? Note that IQs are recorded to the nearest integers.

For a car travelling 60 km per hour (kph), the distance required to brake to stop is normally distributed with mean of 20 meters and a standard deviation of 3 meters. Suppose you are travelling 60 kph in a residential area and a car moves abruptly into your path at a distance of 25 meters.

a) if you apply your brakes, what is the probability that you will brake to a stop within 18 meters or less?

b) if the only way to avoid a collision is to brake to a stop, what is the probability that you will avoid the collision?

A normal random variable X has unknown mean and standard deviation. The probability that X exceeds 4 is 0.9722, and the probability that X exceeds 5 is 0.9332. Find mean and standard deviation.

The finished inside the diameter of a piston ring is normally distributed with a mean of 10 cm and a standard deviation of 0.03 cm.

a) what proportion of rings will have inside diameters exceeding 10.075 cm?

b) what is the probability that a piston ring will have an inside diameter between 9.97 and 10.03 cm?

c) below what value of inside diameter will 15% of the piston rings fall?

Solve the given problem. Dont forget to show your solutions.

1.AA pop fourulstion consist of the four numbers 1,2,4 and 5. List all the possible samples of sizes n=3 wich can be drawn with replacement from the population. Find the following : a. Population mean b. Population variance c. Population standard deviation d. Mean of the sampling distribution of sample means e. Variance of the sampling distribution of sample means f standard deviation of the sampling distribution of sample means

Show your solution:

1. If the population of ABM students of Malaya Integrated High School has a mean of 12.45, what

is the mean of the sampling distribution of its mean?

2. If the mean of the sampling distribution is 24.29, what is the mean of the population?

3. If a population of HUMS students of Makabayan National High School has a variance of 6.4,

what is the variance of the sampling distribution of the sample mean if the sample size is 4 and all

the possible samples are drawn with replacements?

4. If the population of STEM students of Siyensiya Stand Alone Senior High School has a standard

deviation of 9.4, what is the standard deviation of the sampling distribution of its means? The

sampling distribution was derived with sample size n=3, and all the possible samples were drawn

with replacements.

5. If the population standard deviation is 5.6, what is the population variance

Suppose a random variable  x is best described by a normal distribution with  μ = 60 and   Find the  z-score that corresponds to the value  x = 63.

Suppose a random variable x is best described by a normal distribution with μ = 60 and Find the z-score that corresponds to the value x = 63.

Let us consider two sections: section 1 contains 7 male and 10 female students, and section 2 contains 9 male and 7 female students. One section is selected at random and then one student is selected from this section. Find the probability that the selected student is male.

Given the following data on the ages of 75 persons in years. Calculate the first four central moments. Age 09.5–14.5 ,14.5–19.5 , 19.5–24.5 , 24.5–29.5 , 29.5–34.5 ,34.5–39.5, 39.5–44.5 , 44.5–49.5

Number of persons: 3,6,8,12,8,6,3,2 Total 75

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