Suppose that the scores on a reading ability test are normally distributed with a mean of 65 and a standard deviation of 8. what proportion of individuals score at least 64 points on this test? round your answer to at least four decimal places.

problem 2 :

the workers' union at a particular university is quite strong. about 94% of all workers employed by the university belong to the workers' union. recently, the workers went on strike, and now a local tv station plans to interview 4 workers (chosen at random) at the university to get their opinions on the strike. what is the probability that exactly 2 of the workers interviewed are union members? round your response to at least three decimal places.

answer my problems asap

1)

2)

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Problem 1

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

And we can find this probability on this way:

Problem 2

Let X the random variable of interest, on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

And we want to find this probability:

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.