The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 50 hours. we can conclude that at least 75% of this brand of bulbs will last between
(a) 1100 and 1300 hours
(b) 1150 and 1250 hours
(c) 1050 and 1350 hours
(d) 1000 and 1400 hours
(e) 950 and 1450 hours

(A) 1100 and 1300 hours

Step-by-step explanation:

In a normal distribution, we can say that 68% of the values is between the range [µ-σ;µ+σ]  with µ = the mean and σ is the standard deviation.

95% of the values are between the range [µ -2σ; µ+2σ] = [1100;1300]

99.7% of the values are between the range [µ -3σ; µ+3σ] = [1050;1350]

To find 75% of the values, we have to use the z-score

for 75% the Z-score = 1.15

This gives the range: [µ -Zσ; µ+Zσ]  ⇒ [1200 - 1.15*50;1200+1.15*50] = [1142.5 ; 1257.5]

We can say that at least 75% (or more) is in the range [1100;1300]

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step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

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