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The lifespans of seals in a particular zoo are normally distributed. The average seal lives
13.8
13.813, point, 8 years; the standard deviation is
3.2
3.23, point, 2 years.
Use the empirical rule
(
68
−
95
−
99.7
%
)
(68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a seal living longer than
7.4
7.47, point, 4 years.

Respuesta :

kudzordzifrancis

Answer:

2.5%

Step-by-step explanation:

It is given that:

lifespans of seals in a particular zoo are normally distributed. The average seal lives 13.8 years and the standard deviation is 3.2 years.

We want to use the empirical rule to estimate the probability of a seal living longer than 7.4

Let's calculate the z-score of 7.4 using

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

[tex]z = \frac{7.4 - 13.8}{3.2} [/tex]

[tex]z = - 2.00[/tex]

According to empirical rule, 95% of the distribution is within 2 standard deviations, i.e (-2 to 2)

So from (-2 to 0), we would have 47.5%

Since we are looking for the area to the left of -2.00 we subtract this from 50%

to get 2.5%

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