Question

The average battery life os an iPhone X is μ=9.52 hours with a standard deviation of σ =1.86 hours.

a) What is the probability that a single iPhone X lasts less than 9.25 hours?

b) What is the probability that a sample of 50 iPhone X phones lasts more than 10 hours?

c) What is the probability that a sample of 50 iPhone X phones lasts between 9.25 and 10 hours?

Answer 1

GIVEN:

Average battery life of iPhone X hours.

Standard deviation of iPhone X

(a) PROBABILITY THAT A SINGLE IPHONE X LASTS LESS THAN 9.25 HOURS :

To find the probability, we convert the raw score into standard score using formula,

Thus the probability that a single iPhone X lasts less than 9.25 hours is,

  

From the Z table, the probability value is the value with corresponding row -0.1 and column 0.05.

The probability that a single iPhone X lasts less than 9.25 hours is .

(b) PROBABILITY THAT A SAMPLE OF 50 IPHONE X LASTS MORE THAN 10 HOURS :

Since the sample size is at least 30, the Central Limit Theorem is applied:

is approximately normally distributed with mean and standard deviation . Thus we use and not when we standardize. Thus the formula is:

Thus the probability that a sample of 50 iPhone X phones lasts more than 10 hours is,

{Since }

From the Z table, the probability value is the value with corresponding row 1.8 and column 0.02.

Thus the probability that a sample of 50 iPhone X phones lasts more than 10 hours is .

(c) PROBABILITY THAT A SAMPLE OF 50 IPHONE X LASTS BETWEEN 9.25 AND 10 HOURS :

Since the sample size is at least 30, the Central Limit Theorem is applied:

is approximately normally distributed with mean and standard deviation . Thus we use and not when we standardize. Thus the formula is:

Thus the probability that a sample of 50 iPhone X phones lasts between 9.25 and 10 hours is,

{Since }

From the Z table, the first value is the value with corresponding row 1.8 and column 0.02 and the second value is the value with corresponding row -1.0 and column 0.03.

  

Thus the probability that a sample of 50 iPhone X phones lasts between 9.25 and 10 hours is .

Z TABLE: