A company makes batteries with an average life span of 300 hours with a standard deviation of 75 hours. Assuming the distribution is approximated by a normal curve fine the probability that the battery will last:(give 4 decimal places for each answer)

1. Less than 250 hours ____

2. Between 225 and 375 hours _

3. More than 400 hours _____

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Respuesta :

bandnerds bandnerds · Answer 1 · 2017-04-29T04:30:42+02:00

1= 33.5 percent
2=51 percent
3=20.2 percent

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erinna erinna · Answer 2 · 2019-07-30T07:50:26+02:00

Answer:

1. [tex]P(X<250)=0.2546[/tex]

2. [tex]P(225<X<375)=0.6826[/tex]

3. [tex]P(X>400)=0.0918[/tex]

Step-by-step explanation:

Given information: Population mean = 300 hours, Standard deviation=75

Let X be the life of battery in hours.

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

(1) The probability that the battery will last less than 250 hours is

[tex]P(X<250)=P(\frac{X-300}{75}<\frac{250-300}{75})[/tex]

[tex]P(X<250)=P(Z<-0.667)[/tex]

[tex]P(X<250)=0.2546[/tex]

Therefore the probability that the battery will last less than 250 hours is 0.2546.

(2) The probability that the battery will last between 225 and 375 hours is

[tex]P(225<X<375)=P(\frac{225-300}{75}<\frac{X-300}{75}<\frac{375-300}{75})[/tex]

[tex]P(225<X<375)=P(-1<Z<1)[/tex]

[tex]P(225<X<375)=P(Z<1)-P(Z<-1)[/tex]

[tex]P(225<X<375)=0.8413-0.1587[/tex]

[tex]P(225<X<375)=0.6826[/tex]

Therefore the probability that the battery will last between 225 and 375 hours is 0.6826.

(3) The probability that the battery will last more than 400 hours is

[tex]P(X>400)=P(\frac{X-300}{75}<\frac{400-300}{75})[/tex]

[tex]P(X>400)=P(Z>1.33)[/tex]

[tex]P(X>400)=1-P(Z<1.33)[/tex]

[tex]P(X>400)=1-0.9082[/tex]

[tex]P(X>400)=0.0918[/tex]

Therefore the probability that the battery will last more than 400 hours is 0.0918.