Question

1)The age of children in kindergarten on the first day of school is uniformly distributed between 4.93 and 5.84 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible.

a. The mean of this distribution is

b. The standard deviation is

c. The probability that the the child will be older than 5 years old?

d. The probability that the child will be between 5.23 and 5.53 years old is

e. If such a child is at the 6th percentile, how old is that child? __years old.

2) today, the waves are crashing onto the beach every 5.6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.6 seconds. Round to 4 decimal places where possible.

a. The mean of this distribution is__ b. The standard deviation is ___ c. The probability that wave will crash onto the beach exactly 0.4 seconds after the person arrives is P(x = 0.4) = __ d. The probability that the wave will crash onto the beach between 1.8 and 3.6 seconds after the person arrives is P(1.8 < x < 3.6) =__ e. The probability that it will take longer than 2.02 seconds for the wave to crash onto the beach after the person arrives is P(x > 2.02) = __ f. Suppose that the person has already been standing at the shoreline for 0.2 seconds without a wave crashing in. Find the probability that it will take between 1.6 and 2.5 seconds for the wave to crash onto the shoreline.--- g. 74% of the time a person will wait at least how long before the wave crashes in?__ seconds. h. Find the minimum for the upper quartile. __seconds.

Answer 1

Q 1) Solution :

Let the random variable X denotes the age of children in kindergarten on the first day of school.

X is uniformly distributed on ( 4.93,5.84) with pdf ,

a) the mean of the distribution is

b) The standard deviation is

c) The probability that the the child will be older than 5 years old is

d) The probability that the child will be between 5.23 and 5.53 years old is

e) If such a child is at the 6th percentile, how old is that child?

Therefore the age of child at 6th percentile is  

Answer: 4.9846 years old.