Question

The distribution of weights of a large group of high school students is normally distributed with mean 55 kg and standard deviation 5 kg. Which of the following is true?a. About 16 percent of the students will be over 60 kg. b. About 2.5 percent will be below 45 kg. c. Half of them can be expected to weigh less than 55 kg. d. About 5 percent will weigh more than 63 kg. e. All the above are true.

Answer 1

a. P(X > 60)

That is P(X > 60) becomes P(Z > 1)

By using the z table the probability is 0.1586 that is 16% approximately.

So option a is true.

b. P(X < 45)

That is P(X < 45) becomes P(Z < -2)

By using table the probability is about 2.5%

So option b is correct.

c. The normal distribution is symmetric about the mean, so half of the data falls below the mean and half will be above the mean. Here mean is 55, so this is the correct option.

d. P(X > 63)

That is P(X > 63) becomes P(Z > 1.6)

By using table the probability is approximately 5%

So option e is correct, that is all of the above are true.