a)The time it takes to bake a Betty Crocker Supermoist Fudge Cake is normally di

Question

a)The time it takes to bake a Betty Crocker Supermoist Fudge Cake is normally distributed with a mean of 35 minutes and a variance of 36 minutes^2. Let baking time, in minutes, be represented by random variable

b)

The hotel room rate in New York City is normally distributed with a mean of $237 per night. Assume that the standard deviation is unknown.

If 26% of the New York City hotel room rates are more than $248 per night, what is the variance? (Remember the label.)

c) 15% of individuals insured by All-Driver Automobile Insurance Company have received at least one traffic ticket.

For a sample of 140 insured individuals, what is the probability that between 15 and 29 of them received at least one ticket?

Explanation / Answer

1) mean = 35 , variance = 36 , std deviation = sqrt(variance) = sqrt(36) = 6

P(X1 < X < 39) = 1 - P(X > 39) - P(X < X1)

By using normal distribution

0.1290 = 1 - P(z> (39 - 35) / 6) - P( (X< X1)

0.1290 = 1- 0.2525 - P(X < X1)

  P(X<X1) = 0.6185

Use z table to find z value

P(z < 0.3) = 0.6185

Hence,

( x1 - 35) / 6 = 0.3

x1 = 36.8

b) mean = 237 , X = 248

By using normal distribution,

P( X > 248) = 0.26

We need to find z value by using z table at 0.26 So, we get, Z value = 0.64

Z = ( X - mean ) / std. deviation

0.64= (248 - 237) / std. deviation

Std. deviation = (248 - 237) /0.64

= 17.19

Variance = 295.41

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