Question

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 160 mobile phone users.

(a)

What is the probability that at least 80 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.)

(b)

What is the probability that at least 85 but less than 90 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.)

(c)

What is the probability that less than 9 of the 160 phone users do not know how often they use their phone? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

Answer 1

	Probability
at least once per hour	0.51
few times per day	0.25
morning and evening	0.08
hardly ever use	0.12
did not know how often	0.04

The binomial distribution is approximated to normal with,

(a)

Let random variable X = number of person use their phone at least once per hour. The required probability is obtained by calculating the z score,

Where,

​​​​​​​

Now,

The probability for the z score is obtained from standard normal distribution table,

(b)

The required probability is,

Where,

​​​​​​​

Now,

The probability for the z score is obtained from standard normal distribution table,

(c)

Let random variable X = number of phone users do not know how often they use their phone. The required probability is obtained by calculating the z score,

Where,

​​​​​​​

Now,

The probability for the z score is obtained from standard normal distribution table,