A consumer mobility report indicates that in a typical day, 51% of users of mobile phones use their phone at least once per hour, 25% use their phone a few times per day, 8% use their phone morning and evening, and 12% hardly ever use their phones. The remaining 4% indicated that they did not know how often they used their mobile phone. Consider a sample of 150 mobile phone users. (a) What is the probability that at least 70 use their phone at least once per hour? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

0.8888 = 88.88% probability that at least 70 use their phone at least once per hour

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that , .

51% of users of mobile phones use their phone at least once per hour.

This means that

Consider a sample of 150 mobile phone users.

This means that

So

What is the probability that at least 70 use their phone at least once per hour?

This is 1 subtracted by the pvalue of Z when X = 70-1 = 69(at least 70 is more than 69). So

has a pvalue of 0.1112

1 - 0.1112 = 0.8888

0.8888 = 88.88% probability that at least 70 use their phone at least once per hour

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation: