Question

A particular fruit's weights are normally distributed, with a mean of 366 grams and a standard deviation of 22 grams.

If you pick 10 fruit at random, what is the probability that their mean weight will be between 343 grams and 383 grams

PLEASE HELP ME HUHUHU I ONY HAVE 15 MINS LEFY

Answer 1

Solution:

Given that , X follows normal distribution with

= 366

= 22

A sample of size n = 10 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 366

SD =      = 22/​10 =   6.95701085237

P(Sample mean is between 343 and 383)

= P(343 < < 383)

= P( < 383) - P( < 343)

= P[( - )/ < (383 - 366)/6.95701085237] - P[( - )/ < (343 - 366)/6.95701085237]

= P[Z < 2.44] - P[Z < -3.31]

=  0.9927 - 0.0005(use z table)

= 0.9922

Answer : 0.9922